The Ambell Company uses batteries from two different manufacturers. Historically, 60% of the batteries are from manufacturer 1, and 90% of these batteries last for over 40 hours. Only 75% of the batteries from manufacturer 2 last for over 40 hours. A battery in a critical tool fails at 32 hours. What is the probability it was from manufacturer 2?
Answers
Answer:
The probability that the battery in a critical tool fails at 32 hours was from manufacturer 2 is 0.625
Step-by-step explanation:
Given that:
60% of the batteries are from manufacturer 1
90% of these batteries last for over 40 hours
Let the number of the battery duration be n = 0.90
Therefore n' = 1 - 0.90 = 0.10
Let p = manufacturer 1 and q = manufacturer 2
q = 1 - p
q = 1 = 0.6
q = 0.4
Thus ; 40% of the batteries are from manufacturer 2
However;
Only 75% of the batteries from manufacturer 2 last for over 40 hours.
Let number of battery duration be m = 0.75
Therefore ; m' = 1 - 0.75 = 0.25
A battery in a critical tool fails at 32 hours.
Thus; the that the battery in a critical tool fails at 32 hours was from manufacturer 2 is:
[tex]= \dfrac{q \times m' }{ p \times n' + q \times m' }[/tex]
[tex]= \dfrac{0.4 \times0.25 }{ (0.6 \times 0.1) + (0.4 \times 0.25 ) }[/tex]
[tex]=\dfrac{0.1}{0.06+ 0.1}[/tex]
[tex]=\dfrac{0.1}{0.16}[/tex]
= 0.625
The probability that the battery in a critical tool fails at 32 hours was from manufacturer 2 is 0.625
The probability that the battery was from manufacturer 2 is 62.5%.
Since the Ambell Company uses batteries from two different manufacturers, and historically, 60% of the batteries are from manufacturer 1, and 90% of these batteries last for over 40 hours, while only 75% of the batteries from manufacturer 2 last for over 40 hours, if a battery in a critical tool fails at 32 hours, to determine what is the probability it was from manufacturer 2 the following calculation must be performed:
You must establish the percentage of failure of the total batteries, and determine what percentage of failures corresponds to each manufacturer. Manufacturer 1 = 60 x 0.1 = 6 Manufacturer 2 = 40 x 0.25 = 10 Total = 16 16 = 100 10 = X 100 x 10/16 = X 62.5 = X
Therefore, the probability that the battery was from manufacturer 2 is 62.5%.
Learn more in https://brainly.com/question/14461509
Related Questions
Luke is organising a camping trip for the youth club. He is looking at the temperature and rainfall charts for Brighton and Newquay. What is the probability of it raining in July in Brighton? Give your answer as a fraction.
Answers
Answer:
The answer is 15.6/31 or 1/2
Step-by-step explanation:
The data in the question is sufficient to find an answer for it.
1. I look at the temperature and rainfall chart for Brighton, United Kingdom.
2. Check for rainy season and dry season.
3. The rainy season lasts approximately 5 months while the dry season (which still has some rainfall) lasts approximately 7 months. All together, 12 months of the calendar year.
4. July happens to fall within the dry season. The temperature and rainfall statistics are observed.
The number of rainfall days is 15.6 and we know there are 31 days in July.
If the approximate number of days it rains in Brighton, in July, is 15.6 then the probability of rainfall in the month is 15.6/31 which is = 0.503 or 0.5
Therefore, there's a 50% chance of having rainfall in Brighton, on any day in the month of July.
In fraction, 0.5 = 1/2
need help thanksssssssss
Answers
Answer:
Volume: 112 m³.
Surface area: 172 m².
Step-by-step explanation:
The volume is the base times height times length. So, the volume will be 2 * 8 * 7 = 16 * 7 = 112 m³.
The surface area is 2lw + 2lh + 2wh. l = 8; w = 7; h = 2.
2(8)(7) + 2(8)(2) + 2(7)(2) = 2 * 56 + 2 * 16 + 2 * 14 = 112 + 32 + 28 = 112 + 60 = 172 m².
Hope this helps!
SOMEONE PLEASE HELP ME!!! I REALLY NEED SOME HELP!!!
Which of the following points is a solution of the inequality y < - lxl?
A. (1, -2)
B. (1, -1)
C. (1, 0)
Answers
Answer:
A. (1, -2)
Step-by-step explanation:
We can substitute the variables of x and y into the inequality of [tex]y < -|x|[/tex].
Let's start with A, -2 being y and 1 being x.
[tex]-2 < - |1|[/tex]
The absolute value of 1 is 1, and negating that gets us -1.
[tex]-2 < -1[/tex]
Indeed, -2 is less than -1! So A is a solution to the inequality.
Let's test the rest of them, just in case.
For B:
[tex]-1 < -|1|[/tex]
Absolute value of 1 is 1, negating it is -1.
[tex]-1<-1[/tex]
-1 is EQUAL to -1, not less than it, so is not a solution to the inequality.
Let's try C.
[tex]0 < -|1|[/tex]
Absolute value of 1 is 1, negating it is -1.
[tex]0 < -1[/tex]
0 is GREATER than -1, so that is not a solution to the inequality.
Hope this helped!
WILL MARK AS BRAINLIEST 4. Suppose there is a card game where you are dealt a hand of three cards. You have already learned that the total number of three-card hands that can be dealt from a deck of 52 cards is: 52C3=52!/49!3! 52C3=22100 Calculate the probability of getting a hand that has exactly two aces in it (A A X). Do this by finding out the number of possible hands that have exactly two aces, and then dividing by the total possible number of three-card hands that is stated above. Part A: Use the multiplication principle to tell the total number of three-card hands (permutations) that can be made with two aces. (2 points) Part B: In the answer from Part I, each two-ace hand got counted twice. For example, A A X got counted as a separate hand from A A X. Since order should not matter in a card hand, these are really the same hand. What is the actual number of two-ace hands (combinations) you can get from a deck of 52 cards?(2 points) Part C: Find the probability of drawing a three-card hand that includes two aces from a deck of 52 cards. Write your answer as a fraction. (2 points)
Answers
Answer:
Part A- 6
Part B- 3
Part C- 3/22100
Step-by-step explanation:
Part A-
Use the permutation formula and plug in 3 for n and 2 for k.
nPr=n!/(n-k)!
3P2=3!/(3-2)!
Simplify.
3P2=3!/1!
3P2=6
Part B-
Use the combination formula and plug in 3 for n and 2 for k.
nCk=n!/k!(n-k)!
3C2=3!/2!(3-2)!
Simplify.
3C2=3!/2!(1!)
3C2=3
Part C-
It is given that the total number of three-card hands that can be dealt from a deck of 52 cards is 22100. Use the fact that the probability of something equals the total successful outcomes over the sample space. In this case the total successful outcomes is 3 and the sample space is 22100.
I believe the answer is 3/22100
I honestly suck at probability but I tried my best.
A manufacturing process that produces electron tubes is known to have a 10% defective rate. Suppose a random sample of 15 tubes is selected from the manufacturing process. a) Find the probability that no more than two defectives are found?
Answers
Answer:
Probability of obtaining no more than two defective tubes = 0.816
Step-by-step explanation:
The Probability of obtaining no more than two defective tubes in a randomly selected sample of 15 tubes is obtained using the binomial distribution formula: nCr × p^r × q^(n -r).
Where n is number of samples;
r is maximum number of defective tubes, r ≤ 2;
p is probability of defective tubes = 10% or 0.1
q is probability of non-defective tubes, q = 1 - p
Further explanations and calculations are given in the attachment below:
Bart bought a digital camera with a list price of $219 from an online store offering a 6 percent discount. He needs to pay $7.50 for shipping. What was Bart's total cost? A. $205.86 B. $211.50 C. $213.36
Answers
Answer:
Barts total cost is (c)213.36
Step-by-step explanation:
First, you subtract 6% from $219
=204.92
add shipping,
+7.50
=213.36
Hope this helps <3
Answer:
C. $213.36
Step-by-step explanation:
The original price is $219 and the discount is 6% which is equal to $13.14
$219 - $13.14 + $7.50 (shipping cost) = $213.36
Copy the problem, mark the givens in the diagram. Given: CS ≅ HR, ∠CHS ≅ ∠HCR, ∠CSH ≅ ∠HRC, Prove: CR ≅ HS
Help urgently needed
Answers
Explanation:
1. CS ≅ HR, ∠CHS ≅ ∠HCR, ∠CSH ≅ ∠HRC — given
2. ∆CRH ~ ∆HSC — AA similarity theorem
3. ∠SCH ≅ ∠RHC — corresponding angles of similar triangles are congruent
4. CH ≅ HC — reflexive property of congruence
5. ∆CRH ≅ ∆HSC — SAS congruence theorem
6. CR ≅ HS — CPCTC
2) A basketball player scores 70% of his shots on average. What is the probability that he scores at least 18 successful shots tonight if he gets 20 shots?
Answers
Answer:
3.54%
Step-by-step explanation:
This question represents a binomial distribution. A binomial distribution is given by:
[tex]P(x)=\frac{n!}{(n-x)!x!} p^xq^{n-x}[/tex]
Where n is the total number of trials, p is the probability of success, q is the probability of failure and x is the number of success.
Given that:
A basketball player scores 70% of his shots on average, therefore p = 70% = 0.7. Also q = 1 - p = 1 - 0.7 = 0.3.
The total number of trials (n) = 20 shots
The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20)
P(x = 18) = [tex]\frac{20!}{(20-18)!18!}*0.7^{18}*0.3^{20-18}=0.0278[/tex]
P(x = 19) = [tex]\frac{20!}{(20-19)!19!}*0.7^{19}*0.3^{20-19}=0.0068[/tex]
P(x = 20) = [tex]\frac{20!}{(20-20)!20!}*0.7^{20}*0.3^{20-20}=0.0008[/tex]
The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20) = 0.0278 + 0.0068 + 0.0008 = 0.0354 = 3.54%
I need help with this !!
Answers
Answer:
A
Step-by-step explanation:
When subtracting 7 on the left of the equation, he also needs to subtract 7 from the right of the equation.
Step 2 should be:
⅓X +7 -7= 15 -7
What he is trying to do here by subtracting 7 is to move all the constants, that is numbers without any variables such as x, to one side of the equation.
⅓X= 8
X= 8 ×3
X= 24
Make a decision about the given claim. Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).
Claim: The mean pulse rate (in beats per minute) of students in a large math class is greater than 71. A simple random sample of the students has a mean pulse rate of 71.7. Choose the correct answer below.
A. The sample is unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim.
B. The sample is unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
C. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
D. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim.
Answers
Answer:
The correct option is (D).
Step-by-step explanation:
In this case, we need to test whether the mean pulse rate (in beats per minute) of students in a large math class is greater than 71.
The hypothesis can be defined as follows:
H₀: The mean pulse rate of students in a large math class is not greater than 71, i.e. μ ≤ 71.
Hₐ: The mean pulse rate of students in a large math class is greater than 71, i.e. μ > 71.
It is provided that the sample mean pulse rate, of a simple random sample of the students is 71.7.
The sample mean is not very different from the population mean.
So, it cannot be said in confidence that the sample is unusual.
Thus, the correct option is (D).
"The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim."
How to calculate a circumference of a circle?
Answers
Answer: Pi multiplied by the diameter of the circle
Step-by-step explanation:
Answer:
The formula for finding the circumference of a circle is [tex]C = 2\pi r[/tex]. You substitute the radius of the circle for [tex]r[/tex] and multiply it by [tex]2\pi[/tex].
A lottery game has balls numbered 1 through 21. What is the probability of selecting an even numbered ball or an 8? Round to nearest thousandth
Answers
Answer: 0.476
Step-by-step explanation:
Let A = Event of choosing an even number ball.
B = Event of choosing an 8 .
Given, A lottery game has balls numbered 1 through 21.
Sample space: S= {1,2,3,4,5,6,7,8,...., 21}
n(S) = 21
Then, A= {2,4,6,8, 10,...(20)}
i.e. n(A)= 10
B= {8}
n(B) = 1
A∪B = {2,4,6,8, 10,...(20)} = A
n(A∪B)=10
Now, the probability of selecting an even numbered ball or an 8 is
[tex]P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}[/tex]
[tex]=\dfrac{10}{21}\approx0.476[/tex]
Hence, the required probability =0.476
The cost of plastering the 4 walls of a room which is 4m high and breadth one third of its length is Rs. 640 at the rate of Rs. 5/m². What will be the cost of carpeting its floor at the rate of Rs. 250/m².
Answers
Answer:
Rs. 32,000
Step-by-step explanation:
height = 4m
let length = x m
breadth = x/3 m
Area of the 4 walls = 2(length × height) + 2(breadth × height)
Area = 2(4×x) + 2(4 × x/3) = 8x + (8x)/3
Area = (32x)/3 m²
1 m² = Rs. 5
The cost for an area that is (32x)/3 m²= (32x)/3 × 5 Rs.
The cost of plastering 4 walls at Rs.5 per m² = 640
(32x)/3 × 5 = 640
(160x)/3 = 640
x = length = 12
Area = (32x)/3 m² = (32×12)/3 = 128m²
The cost of carpeting its floor at the rate of Rs. 250/m²:
= 128m² × Rs. 250/m² = 32,000
The cost of carpeting its floor at the rate of Rs. 250/m² = Rs. 32,000
Find the largest integer which belongs to the following interval: [−∞, 31]
Answers
Answer:
Largest integer in the interval [−∞, 31] is 31.
Step-by-step explanation:
Given the interval: [−∞, 31]
To find: The largest integer in this interval.
Solution:
First of all, let us learn about the representation of intervals.
Two kind of brackets can be used to represent the intervals. i.e. () and [].
Round bracket means not included in the interval and square bracket means included in the interval.
Also, any combination can also be used.
Let us discuss one by one.
1. [p, q] It means the interval contains the values between p and q. Furthermore, p and q are also included in the interval.
Smallest p
Largest q
2. (p, q) It means the interval contains the values between p and q. Furthermore, p and q are not included in the interval.
Smallest value just greater than p.
Largest value just smaller than q.
3. [p, q) It means the interval contains the values between p and q. Furthermore, p is included in the interval but q is not included in the interval.
Smallest value p.
Largest value just smaller than q.
4. (p, q] It means the interval contains the values between p and q. Furthermore, p is not included in the interval but q is included in the interval.
Smallest value just greater than p.
Largest value q.
As per above explanation, we can clearly observe that:
The largest integer which belongs to the following interval: [−∞, 31] is 31.
Find the slope of the line passing through the points (-3, -8) and (4,6).
Answers
Answer:
slope = 2Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have
[tex](-3;\ -8)\to x_1=-3;\ y_1=-8\\(4;\ 6)\to x_2=4;\ y_2=6[/tex]
Substitute:
[tex]m=\dfrac{6-(-8)}{4-(-3)}=\dfrac{6+8}{4+3}=\dfrac{14}{7}=2[/tex]
The formula for the slope m of the line that passes through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is the following:
[tex]m=\dfrac{y_1-y_2}{x_1-x_2}[/tex]
We have points (4,6) and (-3,-8). Let's plug these values into the formula for slope:
[tex]m=\dfrac{6-(-8)}{4-(-3)}[/tex]
[tex]=\dfrac{14}{7}=2[/tex]
The slope of the line passing through the two points is 2. Let me know if you need any clarifications, thanks!
Which sequence of transformations on preimage Triangle ABC will NOT produce the image A’B’C’
Answers
Answer:
b
Step-by-step explanation:
3 + 5x, for x = 10
A. 350
B. 120
C. 53
D. 75
Answers
Answer:C
Step-by-step explanation:
Pemdas
3+5(10)
5*10=50
3+50=53
A circle is centered at CC-1, -3) and has a radius of 6.
Where does the point P(-6, -6) lie?
Choose 1 answer:
Inside the circle
On the circle
Outside the circle
Answers
Answer:
outside the circle i think
Step-by-step explanation:
Answer:
inside the circle
Step-by-step explanation:
The solutions to the inequality ys-x+1 are shaded on
the graph. Which point is a solution?
(2, 3)
(3,-2)
(2.1)
(-1,3)
Answers
Answer:
the solutions to the inequality ys-x+1 are shaded on the graph. which point is B. (3 ,-2)
All sides of the building shown above meet at right angles. If three of the sides measure 2 meters, 7 meters, and 11 meters as shown, then what is the perimeter of the building in meters?
Answers
Answer:
Perimeter= 40 units
Step-by-step explanation:
Ok
We are asked to look for the perimeter.
We have some clue given.
All at right angle and some sides are given it's full length.
We have the bae to be 11 unit
The height to be 7 unit.
What this mean is that taking either the base or the height should sum up to either 11 or 7 respectively.
Let's go for the other side of the height.
Let's take all the vertical height and sum it up to 7 because the right side is equal to 7.
So we have 7+7+11
But it's not complete yet.
We are given a dimension 2.
And the 2 is in two places so it's total 2*2= 4
The two is for a small base .
The base is actually an extra to the 11 of the other base.
So summing up
We have 2*11 + 2*7 + 2*2
Perimeter= 22+14+4
Perimeter= 40 units
25 points will mark brainlest as part of the save nature campaign the city Forest department has decided to grow more trees to kick off the campaign they start by planting 2 pine trees it has been decided that every year they will increase the amount of trees but 1 tree less than the square of the previous year's count which of the following recursives formulas can be used to determine the total number of tree planted in the future assume there is in limited space for trees and n is the number of years of the program's operation
Answers
Answer:
N(n+1) = N(n)^2 - 1, n>=0, N(0) = 2
or equivalently
N(n) = N(n-1)^2 - 1, n>0, N(0) = 2
Step-by-step explanation:
Year 0 = 2 trees
year 1 = 2^2-1 = 3
year 2 = 3^2-1 =8
year 2 = 8^2-1 =63
...
Recursive formula
Let
n = integer year number
N(n) = number of trees to plant in year n
N(n+1) = N(n)^2-1, n>=0, N(0) = 2
or equivalently
N(n) = N(n-1)^2, n>0, N(0) = 2
Whats the options???
aryn needs enough mulch to cover a rectangle flower bed measuring 2 1/4 yd by 3 1/2yd each bag cover 3 square yds and cost $4 how many bags does she need and how much money she need
Answers
Answer:
cars are dum
Step-by-step explanation:
Need Answers ASAP!!!!
Answers
Answer:
15.9degrees
Step-by-step explanation:
in photo above
Answer:
[tex]\boxed{15.95\°}[/tex]
Step-by-step explanation:
The angle can be found by using trigonometric functions.
tan (θ) = [tex]\frac{opposite}{adjacent}[/tex]
tan (θ) = [tex]\frac{4}{14}[/tex]
θ = [tex]tan^{-1} \frac{4}{14}[/tex]
θ = 15.9453959
θ ≈ 15.95
Mai invests $20,000 at age 20. She hopes the investment will be worth $500,000 when she turns 40. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal? Round to the nearest tenth of a percent.
Answers
Answer:16.1%
Step-by-step explanation:
Answer:
The investment needs the rate of growth to be approximately 16.1%.
Step-by-step explanation:
How many real roots and how many complex roots exist for the polynomial
F(x) - X4+ x2 - 5x2 + x -- 6?
O A. 2 real roots and 2 complex roots
B. O real roots and 4 complex roots
O c. 3 real roots and 1 complex root
D. 4 real roots and 0 complex roots
Answers
Answer:
D. 4 real roots and 0 complex roots
Step-by-step explanation:
If I assume that the function you are saying is
[tex]F(x)=x^4+x^3-5x^2+x-6[/tex]
There should be up to "4 roots," there can't be more or less than 4 total solutions. First, we need to check how many sign changes are there in this function. There are 3 positive real roots. Now lets check for negative roots.
[tex]F(-x)=x^4-x^3-5x^2-x-6[/tex]
There are is only 1 negative real root. Since we basically have 4 real roots, and the max is 4. There should be 4 real roots and 0 complex roots.
Please help
ASAP
ANSWERS
A-48.21
B-66.35
C-53.68
D-28.34
Answers
Answer:
B
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos54° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{39}{AB}[/tex] ( multiply both sides by AB )
AB × cos54° = 39 ( divide both sides by cos54° )
AB = [tex]\frac{39}{cos54}[/tex] ≈ 66.35 → B
Nearsightedness: It is believed that nearsightedness affects about 8% of all children. In a random sample of 194 children, 21 are nearsighted.
(a) What proportion of children in this sample are nearsighted?
(b) Construct hypotheses appropriate for the following question: do these data provide evidence that the 8% value is inaccurate?
(c) Given that the standard error of the sample proportion is 0.0195 and the point estimate follows a nearly normal distribution, calculate the test statistic (the Z statistic).
(d) What is the p-value for this hypothesis test?
(e) What is the conclusion of the hypothesis test?
Answers
Answer:
a)the proportion of student is 0.1082
b)
H1: p = .08
H2: p not equal to 0.08
H1: p =0 .08
H2: p < .08
H1: p =0 .08
H2: p >0 .08
c)z=1.45
d) the p value is 0.1470
e)null hypothesis cannot be accepted,There is no enough evidence to reject the null hypothesis.
Step-by-step explanation:
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
What is the measure of x?
Answers
Answer:
9 in.
Step-by-step explanation:
Given that the line 10 in. and line 4 in. are parallel, then the two triangles are similar.
As such, the ratio of the sides would give the same results.
Hence,
4/6 = 10/(6 + x)
cross multiplying
4(6 + x) = 60
Dividing both sides by 4
6 + x = 15
collecting like terms
x = 15 - 6
= 9
Is 3 a solution to the equation 6x – 7 = 12?
Answers
Answer:
3 is not a solution
Step-by-step explanation:
6x – 7 = 12?
Substitute 3 in for x and see if the equation is true
6*3 - 7 = 12
18-7 = 12
11 =12
This is false so 3 is not a solution
6x = 12 +7
6x = 19
x = 19 / 6
x = 3.2 (1 dp)
I HOPE THIS HELPS:)
Plz help answer a - d 1. Miguel is playing a game in which a box contains four chips with numbers written on them two of the chips have the number one one chip has the number three and the other chip has the number 5 Miguel must choose to chips if both chips have the same number he wants to dollars if the two chipsy chooses have different numbers he loses $1 (-$1) Look at pictures for the questions
Answers
Answer:
Step-by-step explanation:
Hello!
Miguel has four chips, two have the number "1", one has the number "3" and the other has the number "5"
If the experiment is "choosing two chips and looking at their numbers" there are the following possible outcomes:
S= {(1,1)(1,3)(1,5)(3,1)(5,1)(3,5)(5,3)}
The sample space for the experiment has 7 possible combinations.
a)
Be X: the amount of money Miguel will receive or owe.
If two chips with the same number are chosen he will receive $2
If the chips have different number he will owe $1
Looking at the possible outcomes listed above, out of the 7, in only one he will select the same number (1,1)
So the probability of him receiving $2 will be 1/7
Now out of the 7 possible outcomes, 6 will make Miguel owe $1, so you can calculate its probability as: 6/7
xi | $2 | -$1
P(xi) | 1/7 | 6/7
b)
To calculate the expected value or mean you have to use the following formula:
[tex]\frac{}{X}[/tex]= ∑[xi*P(xi)]= (2*1/7)(-1*6/7)= -4/7= $-0.57
c)
The expected value is $-0.57, meaning that Miguel can expect to owe $0.57 at the end of the game.
d)
To make the game fair you have to increase the probability of obtaining two chips with the same number. Any probability close to 50% will make the game easier. For example if you change the experiment so that for earning $2 the probability is 4/7 and for owing $1 the probability is 3/7, the expected earnings will be:
(2*4/7)+(-1*3/7)= $0.71
I hope this helps!