(a) Probability that both numbers are odd = 0.4932
(b) Probability that both numbers are less than 12 = 0.4545
(c) Probability that the same number is chosen twice = 1/60
(a) To find the probability that both numbers are odd, we need to count the number of ways to choose two odd numbers between 1 and 60, and divide by the total number of possible outcomes.
There are 30 odd numbers between 1 and 60, so there are 30 choices for the first number and 29 choices for the second number (since the two numbers can be the same). The total number of possible outcomes is 60 choose 2, which is
60 choose 2 = (60 × 59) / 2 = 1770
So the probability that both numbers are odd is
(30 × 29) / 1770 = 0.4932
(b) To find the probability that both numbers are less than 12, we need to count the number of ways to choose two numbers between 1 and 11, and divide by the total number of possible outcomes.
There are 11 choices for each number, so there are 11 × 11 = 121 possible outcomes. The number of ways to choose two numbers less than 12 is
11 choose 2 = (11 × 10) / 2 = 55
So the probability that both numbers are less than 12 is
55 / 121 = 0.4545
(c) To find the probability that the same number is chosen twice, we need to count the number of ways to choose a number, and then multiply by the probability that the same number is chosen again.
There are 60 choices for the first number, and only 1 choice for the second number if we want it to be the same as the first. So the probability that the same number is chosen twice is
1/60
So the probability that the same number is chosen twice is
(1/60) × 60 = 1/60
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Given that New Mexico has a population of about 12 people per square miles and
an area of about 120,000 square miles, what is the population of New Mexico
Mark only one oval.
10,000
1,000,000
1,440,000
2,400,000
Answer:
1440000
Step-by-step explanation:
Since for every mile, there are 12 people, we have 120000 miles. If we multiply 12 by 120000, we get 1440000.
if you are in a club with 14 people that is organizing a spaghetti dinner, how many different ways can you select 3 people to be ticket takers?
If there are 14 people in a club organizing a spaghetti dinner, there can be 364 ways to select 3 people to be ticket takers.
A combination is a selection of things taken from a larger group, where the order in which things are selected is unimportant. A combination is distinct from a permutation, which is a method of organizing objects in which order matters. A combination is a method of selecting things in which order does not matter. In general, the combination formula can be used to determine the number of possible combinations that exist for a given set of things.
Suppose we have to select 3 people out of 14 people. The number of possible combinations can be found using the combination formula, which is given byC(n,r) = n!/(n-r)!r!where n is the total number of objects, and r is the number of objects selected.C(14,3) = 14!/(14-3)!3!C(14,3) = (14 × 13 × 12)/(3 × 2 × 1)C(14,3) = 364Therefore, there are 364 ways to select 3 people to be ticket takers from a group of 14 people.
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given the arithmetic sequence what is the domain for N?
The domain for n in the arithmetic sequence is the one in the first option:
all integers where n ≥1
What is the domain of N?We have a arithmetic sequence defined by the general formula:
aₙ = 4 - 3*(n - 1)
And we want to find the domain for the possible values of n that we can use in that formula.
Remember that the terms of a sequence are defined as:
a₁, a₂, a₃,...
So the values of n are positive whole numbers, in this case the first one is n = 1.
a₁ = 4 + 3*(1 - 1)
a₁ = 4
And then we can keep using any positive integer, then the correct option is:
all integers where n ≥1
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Simplify (4x3y − 5x2y + 6y) − (9x3y − 3x2y − 6y).
The simplified expression is −5x³y − 2x²y + 12y.
The given expression is (4x³y − 5x²y + 6y) − (9x³y − 3x²y − 6y). To simplify this expression, we need to distribute the negative sign inside the second set of parentheses and then combine like terms.
Distributing the negative sign inside the second set of parentheses, we get:
(4x³y − 5x²y + 6y) − 9x³y + 3x²y + 6y
Next, we can group the terms that have the same variables and exponents:
4x³y − 9x³y = −5x³y −5x²y + 3x²y = −2x²y 6y + 6y = 12y
Finally, we can combine the like terms to obtain the simplified expression:
−5x³y − 2x²y + 12y
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Answer:
B:−5x3y − 2x2y + 12y
Step-by-step explanation:
i took the test and got it right
two people start from the same point. one walks east at 9 mi/h and the other walks northeast at 8 mi/h. how fast is the distance between the people changing after 15 minutes? (round your answer to three decimal places.) mi/h
The distance between the two people is changing at a rate of 24.884 mi/h after 15 minutes.
We can use the Pythagorean theorem to determine the distance between the two people as a function of time. Let x be the distance traveled by the person walking east, and y be the distance traveled by the person walking northeast. Then, after 15 minutes (or 0.25 hours), we have:
x = (9 mi/h) * (0.25 h) = 2.25 mi
y = (8 mi/h) * (0.25 h) = 2 mi
The distance between the two people is given by:
[tex]d = sqrt(x^2 + y^2)[/tex]
Taking the derivative with respect to time t, we get:
[tex]d' = (2x dx/dt + 2y dy/dt) / (2sqrt(x^2 + y^2))[/tex]
Substituting the values we found earlier, we get:
[tex]d' = (2(2.25)(9) + 2(2)(8)) / (2sqrt((2.25)^2 + (2)^2))= 24.884 mi/h[/tex]
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Martha has read 52 pages of her book. This is
20% of the book. How many pages does the
book have?
find the missing value to the nearest hundredth cos__=7/18
67.11
37.67
22.89
21.25
The missing value is approximately 64.12 degrees, which is closest to option D: 21.25 using inverse cos.
The inverse cosine (or arccosine) of both sides of the equation must be taken in order to locate the missing value in the equation cos = 7/18 to the closest tenth. We will then be able to convert the value of to degrees and round it to the closest hundredth using the value of the radian that is produced.
cos θ = 7/18
= arccos(7, 18, 7)
A 1.1181 radian angle
We can use the conversion factor /180 to convert radians to degrees.
θ = 1.1181 × 180/π
64.12 degrees.
As a result, the figure that is lacking is roughly 64.12 degrees, which is closest to choice D: 21.25.
Due to the periodic nature of the cosine function, there are often two solutions when determining the inverse cosine of a value. But, since the problem states that we should round to the closest hundredth, which suggests a single answer, we can disregard the second option in this instance. By reinserting the value we discovered into the original equation and making sure it equals 7/18, we can further confirm that the result is accurate.
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If a bus car 1km and 2 minutes what is the m/s
the speed of the bus in meters per second is 8.33 m/s. If a bus travels a distance of 1 kilometer in 2 minutes, we can use the formula for speed to calculate its speed in meters per second (m/s).
The formula for speed is:
Speed = Distance ÷ Time
Here, the distance is 1 kilometer, which is equal to 1000 meters (since 1 kilometer = 1000 meters), and the time is 2 minutes, which is equal to 120 seconds (since 1 minute = 60 seconds).
So, we can plug these values into the formula:
Speed = 1000 meters ÷ 120 seconds
Simplifying this expression, we get:
Speed = 8.33 meters per second (rounded to two decimal places)
Therefore, the speed of the bus in meters per second is 8.33 m/s.
To put this into context, it's important to understand that speed is the rate at which an object moves, while velocity is the rate at which it moves in a specific direction. So, in this case, we have only calculated the speed of the bus, not its velocity. However, knowing the speed of the bus can be useful for a variety of applications, such as determining how long it will take to travel a certain distance, or calculating the fuel efficiency of the vehicle
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Kayleigh babysat for 11 hours this week. That was 5 fewer than 2/3 as many hours as she babysat last week, H. Write an equation to represent the number of hours she babysat each week.
Answer:
⅔h – 5 = 11
Step-by-step explanation:
h = babysitting hours last week
⅔h = two-thirds of those hours
⅔h - 5 = five hours fewer than two-thirds of those hours
⅔h – 5 = 11
The equation is ⅔h – 5 = 11.
A bag contains 6 red marbles and 1 blue marble. A marble is taken at random, put to one side, and then another marble is taken at random. What is the probability that at least one of the marbles takes was blue?
Give your answer as a fraction in its simplest form
We have 6 red and 1 blue marble thus the probability of drawing blue marble = 1/7
To understand probability as a concept, pay attention to the steps below.
Step 1. Multiply the individual probabilities to obtain the chance of numerous separate events.
Step 2. As there are two separate events in this scenario, double the probabilities of each.
Step 3. Add the individual probabilities to obtain the chance of several events that are mutually exclusive.
In this bag of 7 marbles, there is 1 blue one. Assume that each is marked with a number. Choosing blue-1 has a 1/7 chance of happening. (Why? As there are 7 marbles that may be chosen, each with an equal probability, and since those 7 occurrences are mutually exclusive, the 7 probabilities total up to 1.)
The probability of choosing blue-2 is similarly 1/7; the same goes for blue-3,..., and blue-8. To determine the likelihood of picking a blue, add those up (and blue).
Step 4. Do the same for red next.
Thus the probability of drawing blue marble = 1/7
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what is the center od dilation type ( Number, number)
the center of dilation for the triangle is (0,0)
Define center of dilationThe center of dilation is a point in a plane about which a dilation, a type of transformation, is performed. A dilation is a transformation that changes the size of a geometric figure, while preserving its shape and orientation. The center of dilation is the fixed point that serves as the reference for the scaling or shrinking of the figure.
In a dilation, each point of the original figure is moved away from or towards the center of dilation, by a certain factor called the scale factor.
The coordinate of yellow triangle and scaled triangle both passes through center of axes.
So, the center of dilation is (0,0).
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Can yall help me out?
the answer is A: 63 square units
Answer:
A (Im not entirely sure if this is correct)
Step-by-step explanation:
how I got this answer is: I found the area of the two triangles which was 12.5 (because the area of a triangle is 1/2(b*h) and the base is 3 and the height is 7 then you divide that by two) and I added them up to get 21. Then you would multiply 3 by two because a triangle is half of a rectangle and you would do b*h for a rectangle area and then multiply that by 7 ot get 42 and you would add taht to 21 to get 63
Problem
You're playing a game where you defend your village from an orc invasion. There are
3
33 characters (elf, hobbit, or human) and
5
55 defense tools (magic, sword, shield, slingshot, or umbrella) to pick from.
Answer: 2+ 2
Step-by-step explanation:
no problem
Who can help me? This is solving cube root equation help ?
Answer:
22: 2
23: -7
25: 6
26: 3
Let me know if this helped by clicking the help button or if not please comment with issues and I'll get right back to you!
Step-by-step explanation:
For 22: 2 * 2 * 2 = 8, therefore, 2
For 23: -7 * -7 * -7 = -343. This results in a negative number because there is is an odd number of negative numbers (follows the odd-even negative rule).
For 25: Multiply both sides of the equation by -1/2 to get z^3 = 216. The cube root of 216 is 6
For 26: Add 11 to both sides to get 2h^3 = 54. Divide both sides by 2 to get h^3 = 27. Cube root of 27 is 3.
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kadeesha has a bag of candy full of 10 strawberry chews and 10 cherry chews that she eats one at a time. which word or phrase describes the probability that she reaches in without looking and pulls out a strawberry or a cherry chew?
P(strawberry or cherry) = P (strawberry) + P (cherry) = 1/2 + 1/2 = 1
The probability that Kadeesha reaches in without looking and pulls out a strawberry or a cherry chew is the same and is equal to 50%. This is because there are an equal number of strawberry chews (10) and cherry chews (10) in the bag of candy. Therefore, the probability of her selecting one of either is 1/2 = 0.5 = 50%.
The word or phrase that describes the probability that Kadeesha reaches in without looking and pulls out a strawberry or a cherry chew is "either/or probability".Explanation:The candy bag of Kadeesha contains 10 strawberry chews and 10 cherry chews. This means there are two flavors of candies in the bag. The probability that she picks a strawberry chew at random without looking will be 10/20, which can be simplified to 1/2. Similarly, the probability of picking a cherry chew at random without looking will be 10/20, which can also be simplified to 1/2. When considering either of the probabilities, it implies that the probability that she reaches in without looking and pulls out a strawberry or a cherry chew is the sum of the probability of picking a strawberry chew and the probability of picking a cherry chew.i.e. P (strawberry or cherry) = P (strawberry) + P (cherry) = 1/2 + 1/2 = 1Therefore, the probability that Kadeesha reaches in without looking and pulls out a strawberry or a cherry chew is 1, which implies that it is a sure event. Hence, the word or phrase that describes the probability that she reaches in without looking and pulls out a strawberry or a cherry chew is "either/or probability".
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The difference of 18 and 4
Answer:
14
Step-by-step explanation:
all you have to do to find difference is subtract the small number from the bigger number, 18 - 4 = 14
Answer:
14
Step-by-step explanation:
The difference of 18 and 4
18 - 4
14
The sales tax rate is 10%. If Ariana buys a cowboy hat priced at $25, how much tax will she pay?
Answer:
$27.50
Step-by-step explanation:
If the sales tax rate is 10%, then Ariana will pay 10% of the price of the cowboy hat as tax.
To calculate the amount of tax Ariana will pay:
First, we need to calculate the amount of the tax by multiplying the price of the cowboy hat by the sales tax rate: 0.10 x $25 = $2.50
So, the amount of tax that Ariana will pay is $2.50.
Therefore, Ariana will pay $2.50 in tax when she buys the cowboy hat priced at $25. Her total cost will be $25 + $2.50 = $27.50.
Answer:
2.50$
Step-by-step explanation:
Hope that helps ✌
A plant in my garden is growing 2/3 of a foot every 3/4 of a month. How much does it grow per month?
The plant is growing 0.89 feet per month.
To calculate how much a plant grows per month, you need to first convert the measurements into one unit of measurement.
Since the plant is growing 2/3 of a foot every 3/4 of a month,
we can first convert the fractions of a foot and a month into decimal equivalents.
2/3 of a foot is 0.67 feet, and 3/4 of a month is 0.75 months.
We can then calculate the amount of growth per month by dividing the amount of growth per 3/4 of a month by the amount of time that is 3/4 of a month (0.75).
The equation is 0.67 feet / 0.75 months = 0.89 feet per month.
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Simplify: the sum of 6. 6 and 3. 2 all divided by 5 times the quantity of the squared difference of 2 minus 5 plus 6
The simplified form of the expression the sum of 6. 6 and 3. 2 all divided by 5 times the quantity of the squared difference of 2 minus 5 plus 6 is -0.3267
To simplify this expression, we'll work from the inside out, using the order of arithmetic operation
First, we'll evaluate the expression inside the parentheses:
(2 - 5 + 6) = 3
Next, we'll calculate the squared difference of 2 and 5:
(2 - 5)^2 = (-3)^2 = 9
Then, we'll subtract the result from step 2 from the result of step 1:
3 - 9 = -6
Next, we'll calculate the sum of 6.6 and 3.2:
6.6 + 3.2 = 9.8
Finally, we'll divide the result from step 4 by 5 times the result from step 3:
9.8 / (5 × -6) = 9.8 / -30
= -0.3267 (rounded to four decimal places)
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mathematics homework
Answer:
Step-by-step explanation:
(g * h)(24)
gh*24
24gh
An athlete runs 1/3 of a mile every 1/20 hour. At this rate, how far does the athlete run per hour?
Answer: 20/3 mph or 6.667 mph.
Step-by-step explanation:
Since the athlete runs 1/3 of a mile per 1/20 of an hour, to find how much they run in an hour, you multiply both values by 20 to get: the athlete runs 20/3 miles per 20/20 of an hour, or 20/3 miles per hour.
Given the function h(x), find the value of h(-2). h(x) = x² + 4x - 7
Step-by-step explanation:
[tex]{ \tt{h(x) = {x}^{2} + 4x - 7 }}[/tex]
Substitute for x as -2;
[tex]{ \tt{h( - 2) = {( - 2)}^{2} + 4( - 2) - 7}} \\ \\ { \tt{h( - 2) = 4 - 8 - 7}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ { \tt{h( - 2) = - 11}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Answer:-9
Step-by-step explanation:
h(-2)=h(x)
it symbolize that x=-2;
so, we'll replace every x with -2:
-2^2+3*(-2)-7=4-6-7=-9
the height of a parallelogram is 10 feet more than the length of the base. if the area of the parallelogram is 1200 square feet, find the length of the base and the height.
The length of the base of a parallelogram is 30 feet and the height is 40 feet.
Given that the height of a parallelogram is 10 feet more than the length of the base, and the area of the parallelogram is 1200 square feet. We have to find the length of the base and the height. Let the length of the base of a parallelogram be x. Then, the height of the parallelogram = x + 10.
We know that the area of a parallelogram is given by; A = base × height1200 = x(x + 10). Simplify the equation1200 = x² + 10x. Rearrange the equationx² + 10x - 1200 = 0. On solving this quadratic equation, we get; x = 30 and x = -40.
Since the length of the base cannot be negative, therefore, the length of the base is 30 feet. So, the height of the parallelogram is 30 + 10 = 40 feet. Therefore, the length of the base of a parallelogram is 30 feet and the height is 40 feet.
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There are 8 red cards, 6 blue cards, 7 purple cards, and 4 green cards in a hat.
Part A. What is the theoretical probability of drawing a red card from the hat?
Part B. In a trial, a card is drawn from the hat and then replaced 1,150 times. A red card is drawn 437 times. How much greater is the experimental probability than the theoretical probability?
Oh, wait- I figured it out hehe
Part A: The theoretical probability of drawing a red card is 0.32 or 32%.
Part B: The experimental probability of drawing a red card is 0.38 or 38%, and it is 6% greater than the theoretical probability.
Part A: The theoretical probability of drawing a red card from the hat is the number of red cards divided by the total number of cards in the hat:
[tex]P_{red}[/tex] = 8 ÷ (8 + 6 + 7 + 4)
= 8 ÷ 25
= 0.32 or 32%.
Part B: The experimental probability of drawing a red card can be calculated by dividing the number of times a red card was drawn by the total number of trials:
[tex]P_{red}[/tex] = 437 ÷ 1150
= 0.38 or 38%.
The difference between the experimental probability and the theoretical probability can be calculated as follows:
0.38 - 0.32
= 0.06 or 6%
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Please help!
Question below!!
The coordinates for the dilated triangle is obtained as A'(-1, 8), B'(-7, 6), and C'(-7, -4).
What is dilation?
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.
The coordinates point of the triangle is given as -
A (-1,6)
B (-4,5)
C (-4,0)
To dilate triangle ABC by a scale factor of 2 about the point (-1, 4), we can follow these steps -
Translate the triangle so that the center of dilation is at the origin.
We can do this by subtracting (-1, 4) from each vertex -
A' = (-1, 6) - (-1, 4) = (0, 2)
B' = (-4, 5) - (-1, 4) = (-3, 1)
C' = (-4, 0) - (-1, 4) = (-3, -4)
Dilate the translated triangle by multiplying the coordinates of each vertex by the scale factor of 2 -
A'' = 2(0, 2) = (0, 4)
B'' = 2(-3, 1) = (-6, 2)
C'' = 2(-3, -4) = (-6, -8)
Translate the dilated triangle back to its original position by adding (-1, 4) to each vertex -
A'B'C' = A'' + (-1, 4) = (-1, 8)
B'' + (-1, 4) = (-7, 6)
C'' + (-1, 4) = (-7, -4)
Therefore, the coordinates of the dilated triangle A'B'C' are (-1, 8), (-7, 6), and (-7, -4).
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4. O -1 points 15 HW 080 Ask Your The sky Train from the terminal to the Cental car and long-term parking center is supposed to arrive every 6 minutes. The waiting times for the train are known to follow a uniform distrbution Find the 60th percentile for the waiting times (in minutes). Additional Qa Section 5.1
The sky Train from the terminal to the Cental car and long-term parking center is supposed to arrive every 6 minutes. The waiting times for the train are known to follow a uniform distribution. The 60th percentile of the waiting times is 3 minutes.
Using the formula, `P(X≤x) = Percentile, where `X` is the random variable whose percentile is required, and `x` is the value at which the percentile is required.
Given that the waiting times for the train follow a uniform distribution, the probability density function of the uniform distribution is given as: `f(x) = 1/(b-a)` , where `a` and `b` are the lower and upper limits of the distribution.
Now, it is given that the sky train is supposed to arrive every 6 minutes. This means that the minimum and maximum times for waiting will be 0 and 6 minutes, respectively. Hence, `a = 0` and `b = 6`.
Using the formula for the uniform distribution, we have `f(x) = 1/(6 - 0) = 1/6`. Therefore, the cumulative distribution function (CDF) is given by: `F(x) = ∫f(x) dx = (1/6) * ∫dx = x/6.
`Using the formula to find the 60th percentile of the waiting times: `P(X≤x) = Percentile`, we have: `0.6 = P(X≤x)`. Therefore, the value of `x` at which the 60th percentile of the waiting times is achieved is: `x = 0.6 * (b - a) + a = 0.6 * (6 - 0) + 0 = 3`. Thus, the 60th percentile of the waiting times is 3 minutes.
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Please help, will give brainliest for correct answer.
80 points.
Answer:
Step-by-step explanation: DEFINITIONS vvvvv
Transformations
Refers to the movement of objects in the coordinate plane. There are 4 types: Translation, Reflection, Rotation, and Dilation
Reflection
transformation that flips a figure across a line to form its mirror image on the opposite side of the line
Translation
Transformation that slides a figure.
Rotation
A transformation in which a figure is turned around a point
Dilation
A transformation that changes the size of an object, but not the shape.
Congruence
correspondence of parts.
center of dilation
in a dilation, the fixed point about which the figure is enlarged or reduced
similar
Figures that have the same shape but not necessarily the same size
scale factor
The ratio of any two corresponding lengths in two similar geometric figures.
enlargement
a dilation with a scale factor greater than 1. Image will be greater than the pre-image
reduction
a dilation with a scale factor less than 1. Image will be smaller than the pre-image.
remote interior angles
the angles of a triangle that are not adjacent to a given exterior angle
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
Transversal
a line that intersects two or more lines at different points
SAS Theorem (Side-Angle-Side)
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
Angle-Angle-Side (AAS) Theorem
If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
Side-side-side (SSS) Theorem
If the sides of two triangles are in proportion, then the triangles are similar.
Angle-Side-Angle (ASA) Theorem
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
Angle-Angle-Angle (AAA)
does NOT prove triangles congruent because the sides could be different lengths.
Parallel lines
lines in the same plane that never intersect
Please I really need the help I only have 30 minutes left this is my second attempt at this
The correct option is the second one, your supervisor did not divide by the total number of bags.
What mistake did your supervisor did?Here we can see a table with the size of each bag (in grams) and the number of sold bags.
Now, remember that for a set of N numbers {x₁, ..., xₙ} the mean is:
M = (x₁ + x₂ + ...)/N
So the denominator is the amount of elements in the set.
Then here in the denominator we should see the total number of bags sold, which is:
25 + 32 + 40 + 18 = 115
That number should be in the denominator instead of the sum of the masses.
Then the correct option is the second one.
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FIND THE MISSING SIDES OF THE KITE
Picture for more info!
Thank you.
The required sides of kite are √61, √61, √221 and √221 units.
What is Pythagoras theorem?According to the Pythagoras theorem, the square of the hypotenuse in a right-angled triangle equals the total of the squares of the other two sides. The formula for this theorem is c² = a² + b², where c is the hypotenuse and a and b are the triangle's two sides. Pythagoras theory triangles are another name for these triangles.
According to question:In ΔAOD
AD = [tex]\sqrt{5^2+6^2} = \sqrt{61}[/tex] units
In ΔAOB
AB = [tex]\sqrt{5^2+6^2} = \sqrt{61}[/tex] units
In ΔBOC
BC = [tex]\sqrt{5^2+14^2} = \sqrt{221}[/tex] units
In ΔDOC
DC = [tex]\sqrt{5^2+14^2} = \sqrt{221}[/tex] units
Thus, required sides of kite are √61, √61, √221 and √221 units.
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. in a classroom of 30 students, 3 of the students wear wrist watches. (a) if 14 students are selected with replacement, what is the probability that exactly 2 of them wear wrist watches? (b) if 14 students are selected without replacement,
Probability of
=0.0403.
The probability that exactly two of the 14 students selected with replacement will wear wrist watches is 3/30 * 2/29 * 27/28 * 26/27 = 0.0437.
The probability that exactly two of the 14 students selected without replacement will wear wrist watches is 3/30 * 2/29 * 26/28 * 25/27 = 0.0403.
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