Corrupted by their power, the judges running the popular game show America’s Next Top Mathematician have been taking bribes from many of the contestants. During each of two episodes, a given contestant is either allowed to stay on the show or is kicked off. If the contestant has been bribing the judges, she will be allowed to stay with probability 1. If the contestant has not been bribing the judges, she will be allowed to stay with probability 1/3, independent of what happens in earlier episodes. Suppose that 1/4 of the contestants have been bribing the judges. The same contestants bribe the judges in both rounds. (a) If you pick a random contestant who was allowed to stay during the first episode, what is the probability that she was bribing the judges? (b) If you pick a random contestant, what is the probability that she is allowed to stay during both episodes? (c) If you pick a random contestant who was allowed to stay during the first episode, what is the probability that she ge

Answers

Answer 1

Answer:

(a) The probability that a contestant allowed to stay in the first episode is 0.5

(b) The probability that a contestant will be allowed to stay during both is 0.25

Step-by-step explanation:

The given parameters are;

The probability that a contestant who has been bribing the judges will be allowed to stay = 1

The probability that a contestant who has mot been bribing the judges will be allowed to stay = 1/3

The proportion of the contestant that has been bribing the judges = 1/4

The contestant who bribe the judges in the first round = The contestants who bribe the judges in the second round

(a) Let the total number of contestants = x

Therefore;

The number of contestants in the second round = x/4 + 1/3×(x - x/4) = x/2

Which gives that, half of the contestants make it to the second round

The probability that a contestant allowed to stay in the first episode, Pₐ₁, is given as follows;

Probability = (The number of required outcome)/(The number of possible outcome)

∴ Pₐ₁ = (x/4)/(x/2) = 2/4 = 1/2 = 0.5

The probability that a contestant allowed to stay in the first episode = 0.5

(b) The probability that a contestant will be allowed to stay during both episode, Pₐ₁₂ is given as follows;

The number of contestant that will be allowed to stay after each episode = 1/2×(The number contestant in the previous episode)

Therefore;

The number of contestant that will be allowed to stay after the first episode = 1/2 × x = x/2

The number of contestant that will be allowed to stay after the second episode = 1/2 × x/2 = x/4

Therefore, the number of contestant that will be allowed to stay after both episode = x/4

Pₐ₁₂ = (The number of contestant that will be allowed to stay after both episode)/(The total number of contestants)

∴ Pₐ₁₂ = (x/4)/x  = 1/4 = 0.25

The probability that a contestant will be allowed to stay during both = 0.25.


Related Questions

yo please help i have no idea how to do this(the first 2 questions the tecaher did)

Answers

Answer:

Step-by-step explanation:

You'll need to learn the formula for the circumference of a circle.  If the radius is r, the circumference C is C = 2πr.  It appears that your teacher is using pi for the exact circumference and 3.14 for the approximate circumference.

The radius of the first circle is 5 in.  Thus, the exact circumference is

C = 2πr = 2π(5 in) = 10π in, and the approximate circumference is

C = 2(3.14)(5 in) = 31.4 in

In which situation do the quantities combine to make 0?

A-Juan spent $20. The next day, he earned $10 per hour for 2 1/2 hours
of babysitting

B- Erica deposited $75 into her savings account. She withdrew $75 the
following week.


C-The predicted high temperature for a winter day is 7°C and the predicted low temperature is -7°C.


D- A deep-sea diver descends 15 meters, pauses, and then descends another
15 meters.​

Answers

Answer:

B- Erica deposited $75 into her savings account. She withdrew $75 the

following week.

Step-by-step explanation:

Please help I’ll mark you as brainliest if correct

What is the slope of a line perpendicular to the line whose equation is
3x – 12y = 216. Fully reduce your answer.
=

Answers

X=72 Is the answer for your question

Answer:

Step-by-step explanation:

-4

Write an equation that represents the scenario: Taylor’s Tow Truck charges $30 to pick up the car and then an additional 2.50 per mile driven to tow your car.

Answers

Answer:

30+2.50m=t

Step-by-step explanation:

where m represents the amount of miles driven and t represents the total of money owed

can i get brainliest please?

Answer:

joker is not see the following questions and the answers will come up on your site

Four students are determining the probability of flipping a coin and it landing head's up. Each flips a coin the number of times shown in the table below.

Student
Number of Flips
Ana
50
Brady
10
Collin
80
Deshawn
20

Which student is most likely to find that the actual number of times his or her coin lands heads up most closely matches the predicted number of heads-up landings?

Answers

Answer:

Collin with 80

Step-by-step explanation:

Because he has the most flips, therefor he can most closely predict the number of heads up landings

Answer:

The correct answer is C.

Step-by-step explanation:

Collin is most likely to find that the actual number of times his coin lands heads up most closely matches the predicted number of heads-up landings.

Hopefully, this helps! :D

Ask your question below!

Cathy buys 7 ounces of dried cherries in bulk. If dried
cherries cost $0.41 per ounce, how much will she pay?
$2.87
B $0.28
C $2.15
D $3.07

Answers

Answer:

A. $2.87

Step-by-step explanation:

A because it’s the answer

please hellp me and give me a real answer! I MARK BRAINLEST

Answers

Answer:

The answer is

X+150 >_ 1000

Find the solution to the system of equations.
You can use the interactive graph below to find the solution.

y = -5x + 6
y = 3x – 2

X=

y =

Answers

Answer:

(1,1)     X=1      Y=1

Step-by-step explanation:

x = 1

y = 1

adding characters for no reason lo

At 5:30 a.m., a thermometer indicates the temperature is 15 degrees below zero Celsius, -15"C. At 11:00 am., a thermometer indicates the temperature is 3 degrees above zero Celsius, 3'C. What integer represents a temperature of 2 degrees below zero Celsius?

Answers

-2 degrees C.

hope this helps!

Gavin doubles it then adds 15 to get the answer 44.2 what was the original number

Answers

Answer:

14.6

Step-by-step explanation:

44.2 - 15 = 29.2

29.2 / 2 = 14.6

Answer:

14.6

Step-by-step explanation:

If you take 44.2 and subtract 15, you get 29.2. You would then just divide 29.2 by 2 to get the original number. You're literally doing the equation backward.

Morgan is in the business of manufacturing phones. She pays a cost of $200 per phone produced for materials and labor and also must pay a daily fixed cost of $400 to rent the building and equipment. Make a table of values and then write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.

Answers

Divide 200 and 400 then bam- your answer is there

A linear equation is an algebraic equation of the form [tex]y=mx+b[/tex]. , where m is the slope and b is the y-intercept.

Total cost represented by equation, [tex]C=200x+400[/tex]

Let number of phones is represented by x .

Since, She pays a cost of $200 per phone produced for materials and labor

For x phones, she will pay = 200x

Since, she also pays daily fixed cost of $400 to rent the building and equipment

Therefore, total cost is represented by equation shown below,

                           [tex]C=200x+400[/tex]

Learn more:

https://brainly.com/question/20335698

3/4x + 2/5 = 4x - 1/4x

Answers

Answer: x=2/15

Ya I think so.

Answer:

4/45 = x

Step-by-step explanation:

Strongly suggest that you enclose the fractional coefficients inside parentheses to reduce possible ambiguity:

(3/4)x + 2/5 = 4x - (1/4)x

Consolidate the x terms on the right side and leave the 2/5 on the left:

2/5 = (4 - 1/4 + 3/4)x, or

2/5 = (4 1/2)x   or 2/5 = (9/2)x

Solving for x:  Multiply both sides by (2/9):

(2/9)(2/5) = (2/9)(9/2)x, or:

4/45 = x

Note:  please include ALL instructions.

What is −15÷3/5?
-25
-9
-1/9
-1/25

Answers

Answer:

-25

Step-by-step explanation:

i took the test

Is each pair of equations equivalent? explain.
4y+2x=-7
2y-6x=8

Answers

No, because 4y+2x=-7 in slope intercept form is y=-1/2x-7/4 and 2y-6x=8 is y=3x+4
Hope this helps if so pls mark brainliest

simplify: log64+2log5-2log40​

Answers

Answer: 0

Step-by-step explanation:

Use rules of logarithms to condense.

which of the lines below is parallel to y = 5x + 7 ?

Answers

Any line with a slope of 5 is parallel, because parallel lines have the same slope.

What are the next two numbers in the sequence?
4, 16, 64, 256,

Answers

Answer:

1024.

Step-by-step explanation:

You just multiply by 4

The amount of money an employee earns is proportional to the number of hours worked. If the employee works 40 hours and earns $1,100, how much does the employee earn per hour?

Answers

Answer: $27.5

Step-by-step explanation:

From the question, we are informed that employee works 40 hours and earns $1,100, to calculate the amount that the employee earn per hour will be:

Amount earned = $1100

Number of hours worked = 40 hours

Amount earned per hour = $1100/40 = $27.5

How many gallons equal 8 quarts?

2 gallons
4 gallons
12 gallons
32 gallon

Answers

its 2 gallons

4 would be 16

12 would be 48

32 would be 128

the answer is 2 gallons

The Rodriguez family spends 18% of their monthly income on going out to eat. What is the equivalent fraction of the family’s budget that is spent going out to eat? ​

Answers

Answer:

9/50

Step-by-step explanation:

If angle J and angle K are vertical angles, J and K are congruent.

Answers

Answer:

Yes they are congruent

Step-by-step explanation:

Hope this helps!!!!!!!

Yes they are congruent

passes through (-6,-1) and is parallel to y=-2/3x+1​

Answers

answer: y = -2/3x - 5

explanation: parallel slopes are the same, so the new equation would have a slope of -2/3. now, we have to find the y-intercept. to do this, plug in the x and y values for our new equation. we know that the standard form is y=mx+b, where b is the y-intercept.
-1 = -2/3(-6) + b
multiply
-1 = 4 + b
subtract 4 on both sides
-5 = b
so our new equation is
y = -2/3x - 5
you can check by plugging in the x-value (-6)
y= -2/3(-6) - 5
to get
y= -1
which makes this correct

Which expression uses the associative property to make it
easier to evaluate 6(1/3•7/5)?
A. (6•5/7)1/3
B. (6•1/3)7/5
C.6(7/5•1/3)
D.3(1/6•7/5)

Answers

Answer:b

Step-by-step explanation:

The associative property for the expression is  (6 • 1/3)7/5.

What are the Properties of Multiplication?

Certain rules that are used while multiplying numbers are known as the characteristics of multiplication. All types of mathematical expressions, whether they be algebraic expressions, fractions, or integers, can be solved thanks to these features, which make it simple to simplify expressions.

Given expression 6(1/3 • 7/5),

to write its associative property

The Associative Property of Multiplication states that altering the way the numbers are grouped has no impact on the result of the multiplication.

a(b . c) = (a . b)c

6(1/3 • 7/5) =  (6 • 1/3)7/5

Hence correct expression for the property is option B,  (6 • 1/3)7/5.

Learn more about the Properties of Multiplication;

https://brainly.com/question/386524

#SPJ5

All of the following expressions are equivalent except _____.

x + (-2)
-2 + x
x - 2
2 - x

Answers

The final one, as all of the twos are negative in the other options

The probability that a randomly-selected person at a show has seen the band play live before is 50%. A "superfan" is defined as someone who has seen the band play live at least 5 times. The probability that a person at a show is a "superfan" is 30%. Two people are selected at random. What is the probability that both people have both seen the band perform live before, and are "superfans?"

Answers

Answer:

0.25 and 0.09

Step-by-step explanation:

The probability that a randomly-selected person at a show has seen the band play live before is 50%=0.50

The probability that a person at a show is a "superfan" is 30%=0.30

Two people are selected at random.

The probability that both people have both seen the band perform live before

= The probability that the first person has seen the band live before and the second person also has seen the band live before.

=0.50 x 0.50

=0.25

Similarly, the probability that both are  "superfans"

=The probability that the first person is a superfan and the probability that the second person is a superfan.

=0.30 x 0.30

=0.09

Hence, the probability that both people have both seen the band perform live before, and are "superfans" are 0.25 and 0.09 respectively.

39.99+0.45x=44.99+0.4x​

Answers

Answer:

x=100

Step-by-step explanation:

39.99+0.45x=44.99+0.4x​

0.45x=5+0.4x    

0.05x=5

x=100

9) There are six girls and 12 boys in Ms. Jeffry's environmental club. She wants to divide the students into groups with the same number of boys and the same number of girls in each group. What is the maximum number of groups she can make? *​

Answers

No . of girls in Ms. Jeffry's environmental club = 6

No . of boys in Ms. Jeffry's environmental club = 12

To find the maximum number of groups she can make , we have to find the highest common factor ( HCF ) of the number of boys and girls in her club .

Factors of 6 = 1 , 2 , 3 and 6

Factors of 12 = 2 , 3 , 4 , 6 and 12

Hence the highest common factor of 6 and 12 are 6 .

Therefore , the maximum number of groups Ms . Jeffry can make where the number of girls and boys are same are 6 .

what is the length of a cube with 27 ft

Answers

Answer:

3

Step-by-step explanation:

27=3^3

=3*3*3

27=27

i think it is clear &i hope it helps you

The domain of this function is {-2, 3). What is the minimum value in
the range of this function?
f(x) = -2x + 5

A: {-1}
B: {9}
C: {11}
D: {-11}

Answers

the answer is D (-11)

hope this helped

if there are 8 boys and 48 girls in a room, fill out all of the possible ratios of boys to girls that could be made?

Answers

Answer:

1:6

Step-by-step explanation:

8:48 the ratio

48/8 = 6  First you divide in this case both sides can be divided by 8, giving the answer in the most simplest form.

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