Question 1

Find the indicated probability.
-A sample of 4 different calculators is randomly selected from a group containing 47 that are defective and 29 that have no defects. What is the probability that all four of the calculators selected are defective? Round to four
Decimal places.
A) 0.1390
B) 0.1463
C) 7.5098
D) 0.1449

Accepted Answer

The probability of selecting a defective calculator on the first selection is 47/76. Since the selection is without replacement, the probability of selecting a defective calculator on the second selection is 46/75, on the third selection is 45/74, and on the fourth selection is 44/73. The probability of all four events occurring together is the product of their individual probabilities: (47/76) * (46/75) * (45/74) * (44/73) = 0.1390 (rounded to four decimal places). Therefore, the best choice is A.

Question 2

Find the indicated probability.
-A study conducted at a certain college shows that 65% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that 11 randomly selected graduates all find jobs in their
Chosen field within a year of graduating. Round to the nearest thousandth if necessary.
A) 0.169
B) 0.009
C) 0.013
D) 7.150

Accepted Answer

This problem involves calculating the probability of a success (finding a job in their chosen field within a year) in a binomial distribution (either they find a job or they don't). The formula for this probability is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the total number of trials, k is the number of success, p is the probability of success, and (n choose k) is the binomial coefficient (the number of ways to choose k from n).

In this case, n = 11, k = 11, p = 0.65, and (n choose k) = 1 (there's only one way to choose all 11 graduates to find a job). Plugging these values into the formula, we get:

P(X = 11) = (11 choose 11) * 0.65^11 * (1-0.65)^(11-11)
P(X = 11) = 1 * 0.65^11 * 0.35^0
P(X = 11) = 0.009205 (rounded to the nearest thousandth)

Therefore, the closest answer choice is B: 0.009.

Question 3

Provide a written description of the complement of the given event.
-When 100 engines are shipped, all of them are free of defects.
A) None of the engines are defective.
B) All of the engines are defective.
C) At least one of the engines is defective.
D) At most one of the engines is defective.

Accepted Answer

The complement of the event "all of the engines are free of defects" is "at least one of the engines is defective". This means that there is at least one engine that is not free of defects. Choice C represents this complement event. Choices A and D are incorrect because they describe the original event itself, not its complement. Choice B is also incorrect as it is the extreme opposite of the original event, and it is unlikely to happen in reality.

Question 4

Find the indicated probability.
-A IRS auditor randomly selects 3 tax returns from 49 returns of which 7 contain errors. What is the probability that she selects none of those containing errors? Round to four decimal places.
A) 0.6231
B) 0.0029
C) 0.6297
D) 0.0019

Accepted Answer

The probability of selecting a return with an error is 7/49. The probability of selecting a return without an error is 42/49. The probability of selecting 3 returns without errors is (42/49)^3 = 0.6231.

Question 5

Find the indicated probability.
-Among the contestants in a competition are 46 women and 23 men. If 5 winners are randomly selected, what is the probability that they are all men? Round to five decimal places.
A) 0.02455
B) 0.13169
C) 0.00299
D) 0.03125

Accepted Answer

The total number of contestants is 69 (46+23). The number of ways to choose 5 winners out of 69 contestants is (69 choose 5). The number of ways to choose 5 men out of 23 is (23 choose 5). Therefore, the probability of choosing 5 men is:

(23 choose 5)/(69 choose 5) = 0.00299 (rounded to five decimal places).

Therefore, the correct answer is C).

Question 6

Provide a written description of the complement of the given event.
-Of ten adults, at least one of them has high blood pressure.
A) All of the adults have high blood pressure.
B) Nine of the adults have high blood pressure.
C) At most one of the adults has high blood pressure.
D) None of the adults have high blood pressure.

Accepted Answer

The complement of the event "at least one of them has high blood pressure" is "none of the adults have high blood pressure". So the best choice is D.

Question 7

Find the indicated probability.
-In a homicide case 4 different witnesses picked the same man from a line up. The line up contained 5 men. If the identifications were made by random guesses, find the probability that all 4 witnesses would pick the same
Person.
A) 0.0009766
B) 0.8
C) 0.0016
D) 0.008

Accepted Answer

The answer of Find the indicated probability.
-In a homicide case...

Question 8

Find the indicated probability.
-When a pair of dice are rolled there are 36 different possible outcomes: 1-1, 1-2, ... 6-6. If a pair of dice are rolled 3 times, what is the probability of getting a sum of 7 every time? Round to eight decimal places.
A) 0.00462963
B) 0.00735168
C) 0.00291545
D) 0.0476

Accepted Answer

There are 6 ways to get a sum of 7 on a pair of dice: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). So the probability of getting a sum of 7 on one roll is 6/36 = 1/6. The probability of getting a sum of 7 on three rolls is (1/6)^3 = 0.00462963.

Question 9

Find the indicated probability.
-In one town, 66% of adults have health insurance. What is the probability that 4 adults selected at random from the town all have health insurance? Round to the nearest thousandth if necessary.
A) 0.66
B) 2.64
C) 0.19
D) 0.061

Accepted Answer

The answer of Find the indicated probability.
-In one town, 66%...

Question 10

Find the indicated probability.
-A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that all of them are acceptable.
A) 2.1
B) 0.429
C) 0.343
D) 0.027

Accepted Answer

The probability that all three products are acceptable is calculated by multiplying the probability of one product being acceptable (0.7) three times: 0.7 * 0.7 * 0.7 = 0.343.

Question 11

Find the indicated probability. Round to the nearest thousandth.
-An unprepared student makes random guesses for the ten true-false questions on a quiz. Find the probability that there is at least one correct answer.
A) 0.001
B) 0.100
C) 0.900
D) 0.999

Accepted Answer

The probability of getting at least one correct answer is 1 minus the probability of getting all answers wrong. The probability of guessing one question wrong is 0.5, so for ten questions, it's 0.5^10 = 0.0009765625. Thus, the probability of at least one correct answer is 1 - 0.0009765625 = 0.999.

Question 12

Find the indicated probability.
-What is the probability that 4 randomly selected people all have different birthdays? Round to four decimal places.
A) 0.9891
B) 0.9918
C) 0.9836
D) 0.9729

Accepted Answer

There are 365 possible birthdays in a year. The probability that the second person has a different birthday than the first is 364/365. The probability that the third person has a different birthday than the first two is 363/365. The probability that the fourth person has a different birthday than the first three is 362/365. Therefore, the probability that all four have different birthdays is (364/365) * (363/365) * (362/365) = 0.9836, rounded to four decimal places.

Question 13

Find the indicated probability.
-The table below describes the smoking habits of a group of asthma sufferers.  If two different people are randomly selected from the 1005 subjects, find the probability that they are both women. Round to four decimal places.
A) 0.000003984
B) 0.1648
C) 0.7517
D) 0.2483

Accepted Answer

The answer of Find the indicated probability.
-The table below describes...

Question 14

Find the indicated probability.
-You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black. Express your answer as a simplified fraction. 
A) $\frac { 1 } { 2,652 }$
B) $\frac { 25 } { 102 }$
C) $\frac { 13 } { 51 }$
D) $\frac { 25 } { 51 }$

Accepted Answer

There are 26 black cards in a deck. The probability the first card is black is 26/52. If the first card is black, there are 25 black cards left out of 51 total cards. So, the probability both cards are black is (26/52) * (25/51) = 25/102.

Question 15

Find the indicated probability.
-The table below describes the smoking habits of a group of asthma sufferers.  If two different people are randomly selected from the 865 subjects, find the probability that they are both heavy smokers. Round to six decimal places.
A) 0.001637
B) 0.0001524
C) 0.9913
D) 0.008671

Accepted Answer

The answer of Find the indicated probability.
-The table below describes...

Question 16

Provide a written description of the complement of the given event.
-Of the thirteen different women Calvin asks for a date, at least one of them accepts.
A) All but one woman accepts Calvin's offer.
B) None of the women accept Calvin's offer.
C) All of the women accept Calvin's offer.
D) At most one of the women accepts Calvin's offer.

Accepted Answer

The complement of the event "at least one of them accepts" is "none of them accept."

Question 17

Provide a written description of the complement of the given event.
-When several textbooks are edited, none of them are found to be free of errors.
A) At least one of the textbooks is free of errors.
B) All of the textbooks are free of errors.
C) At most one of the textbooks is free of errors.
D) One of the textbooks is free of errors.

Accepted Answer

The complement of the event "none of the textbooks are found to be free of errors" is that "at least one of the textbooks is free of errors."

Question 18

Find the indicated probability.
-Find the probability that 3 randomly selected people all have the same birthday. Ignore leap years. Round to eight decimal places.
A) 0.00000002
B) 0.00000751
C) 0.3333
D) 0.0082

Accepted Answer

This is a classic example of the birthday problem in probability. The probability that the first person has a unique birthday is 1. The probability that the second person also has a unique birthday is (364/365), since there are 364 possible unique birthdays left out of 365. The probability that the third person also has a unique birthday is (363/365), since there are 363 possible unique birthdays left out of 365. To find the probability that all three have the same birthday, we subtract the total probability of all three having unique birthdays from 1. Therefore, the probability is:
1 - 1 x (364/365) x (363/365) = 0.00000751 (rounded to 8 decimal places). Thus, the best choice is B.

Question 19

Find the indicated probability.
-A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made.
A) 0.7733
B) 0.7744
C) 0.0144
D) 0.176

Accepted Answer

Since the first selection is replaced before the second is made, we can consider each selection as independent. The probability of selecting a good coil on any given selection is 88/100, and the probability of selecting a defective coil on any given selection is 12/100. 
Therefore, the probability of getting two good coils is (88/100)*(88/100) = 0.7744. Hence, the answer is choice B.

Question 20

Find the indicated probability.
-A bin contains 64 light bulbs of which 10 are defective. If 5 light bulbs are randomly selected from the bin with replacement, find the probability that all the bulbs selected are good ones. Round to the nearest thousandth if
Necessary.
A) 0.484
B) 0.844
C) 0
D) 0.428

Accepted Answer

The probability of selecting a good bulb on any one trial is 54/64. Since replacement is allowed, the 5 trials are independent, so the probability of selecting 5 good bulbs is (54/64)^5 = 0.428 (rounded to three decimal places). Therefore, the correct choice is D.

Quiz 4: Probability

Find the indicated probability. -A sample of 4 different calculators is randomly selected from a group containing 47 that are defective and 29 that have no defects. What is the probability that all four of the calculators selected are defective? Round to four Decimal places.

Provide a written description of the complement of the given event. -When 100 engines are shipped, all of them are free of defects.

Find the indicated probability. -A IRS auditor randomly selects 3 tax returns from 49 returns of which 7 contain errors. What is the probability that she selects none of those containing errors? Round to four decimal places.

Find the indicated probability. -Among the contestants in a competition are 46 women and 23 men. If 5 winners are randomly selected, what is the probability that they are all men? Round to five decimal places.

Provide a written description of the complement of the given event. -Of ten adults, at least one of them has high blood pressure.

Find the indicated probability. -In a homicide case 4 different witnesses picked the same man from a line up. The line up contained 5 men. If the identifications were made by random guesses, find the probability that all 4 witnesses would pick the same Person.

Find the indicated probability. -When a pair of dice are rolled there are 36 different possible outcomes: 1-1, 1-2, ... 6-6. If a pair of dice are rolled 3 times, what is the probability of getting a sum of 7 every time? Round to eight decimal places.

Find the indicated probability. -In one town, 66% of adults have health insurance. What is the probability that 4 adults selected at random from the town all have health insurance? Round to the nearest thousandth if necessary.

Find the indicated probability. -A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that all of them are acceptable.

Find the indicated probability. Round to the nearest thousandth. -An unprepared student makes random guesses for the ten true-false questions on a quiz. Find the probability that there is at least one correct answer.

Find the indicated probability. -What is the probability that 4 randomly selected people all have different birthdays? Round to four decimal places.

Find the indicated probability. -The table below describes the smoking habits of a group of asthma sufferers. If two different people are randomly selected from the 1005 subjects, find the probability that they are both women. Round to four decimal places.

Find the indicated probability. -You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black. Express your answer as a simplified fraction.

Find the indicated probability. -The table below describes the smoking habits of a group of asthma sufferers. If two different people are randomly selected from the 865 subjects, find the probability that they are both heavy smokers. Round to six decimal places.

Provide a written description of the complement of the given event. -Of the thirteen different women Calvin asks for a date, at least one of them accepts.

Provide a written description of the complement of the given event. -When several textbooks are edited, none of them are found to be free of errors.

Find the indicated probability. -Find the probability that 3 randomly selected people all have the same birthday. Ignore leap years. Round to eight decimal places.

Find the indicated probability. -A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made.

Find the indicated probability. -A bin contains 64 light bulbs of which 10 are defective. If 5 light bulbs are randomly selected from the bin with replacement, find the probability that all the bulbs selected are good ones. Round to the nearest thousandth if Necessary.