Question 1

A red ball and 19 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting a red R ball on the first draw and a white W ball on the second? ​
A)Pr(R first ∩ W second) = 
B)Pr(R first ∩ W second) = 
C)Pr(R first ∩ W second) = 
D)Pr(R first ∩ W second) = 
E)Pr(R first ∩ W second) = 1

Accepted Answer

The answer of A red ball and 19 white balls...

Question 2

The following table gives the results of a 2005 survey of 1000 people regarding the funding of universal health care by employers (employer mandate). ​  What is the probability that a person selected at random from this group will favor universal health care F with an employer mandate, given that the person is a Democrat D?
​
A)Pr(F | D) = 
B)Pr(F | D) = 
C)Pr(F | D) = 
D)Pr(F | D) = 
E)Pr(F | D) =

Accepted Answer

The answer of The following table gives the results of...

Question 3

On June 16, 1997, two amateur golfers playing together hit back-to-back holes in one (Source: The Island Packet, June 19, 1997). Suppose the probability of an amateur golfer getting a hole-in-one is  . If the golfers' shots are independent of each other, what is the probability that two amateur golfers will get back-to-back holes in one? ​
A)Pr(hole-in-one ∩ hole-in-one) = 
B)Pr(hole-in-one ∩ hole-in-one) = 
C)Pr(hole-in-one ∩ hole-in-one) = 
D)Pr(hole-in-one ∩ hole-in-one) = 
E)Pr(hole-in-one ∩ hole-in-one) =

Accepted Answer

The answer of On June 16, 1997, two amateur golfers...

Question 4

Forty-eight percent of the U.S. population is female, and 23.3% of the female population have a college degree. If a U.S. resident is chosen at random, what is the probability, to three decimal places, that the person is a female with a college degree? ​
A)Pr(female ∩ college degree) = 0.233
B)Pr(female ∩ college degree) = 0.713
C)Pr(female ∩ college degree) = 0.023
D)Pr(female ∩ college degree) = 0.112
E)Pr(female ∩ college degree) = 0.048

Accepted Answer

To find the probability that a randomly chosen U.S. resident is a female with a college degree, multiply the probability of being female (0.48) by the probability that a female has a college degree (0.233): $0.48 \times 0.233 = 0.11184$, which rounds to 0.112 to three decimal places.

Question 5

An unprepared student must take a 7-question, multiple-choice test that has 5 possible answers per question. If the student can eliminate 1 of the possible answers on the first 5 questions, and if she guesses on every question, what is the probability that she will answer every question incorrectly? ​
A)Pr(all incorrect) = 
B)Pr(all incorrect) = 
C)Pr(all incorrect) = 
D)Pr(all incorrect) = 
E)Pr(all incorrect) =

Accepted Answer

The answer of An unprepared student must take a 7-question,...

Question 6

A bag contains 3 nickels, 5 dimes, and 4 quarters. If you draw 3 coins at random from the bag, without replacement, what is the probability that you will get a nickel N, a quarter Q, and a nickel N, in that order? ​
A)Pr(N first ∩ Q second ∩ N third) = 
B)Pr(N first ∩ Q second ∩ N third) = 
C)Pr(N first ∩ Q second ∩ N third) = 
D)Pr(N first ∩ Q second ∩ N third) = 
E)Pr(N first ∩ Q second ∩ N third) =

Accepted Answer

The answer of A bag contains 3 nickels, 5 dimes,...

Question 7

Two balls are drawn, without replacement, from a bag containing 18 blue balls numbered 1-18 and 4 green balls numbered 19-22. What is the probability that the first ball is blue and even-numbered and the second ball is even-numbered? ​
A) 
B) 
C)0
D) 
E)

Accepted Answer

The answer of Two balls are drawn, without replacement, from...

Question 8

Suppose the following table summarizes the opinions of various groups on the issue of increased military spending. ​  ​
Given that a randomly selected individual is nonwhite NW, find the probability that he or she opposes increased military spending O.
​
A)​Pr(O | NW) = 
B)​​Pr(O | NW) = 
C)​​Pr(O | NW) = 
D)​​Pr(O | NW) = 
E)​​Pr(O | NW) =

Accepted Answer

The answer of Suppose the following table summarizes the opinions...

Question 9

If 5% of all light bulbs a company manufactures are defective, the probability of any one bulb being defective is 0.05. What is the probability that four bulbs drawn independently from the company's stock will be defective? Round your answer to eight decimal places. ​
A)0.06250000
B)0.00000031
C)0.00012500
D)0.00000625
E)0.00000000

Accepted Answer

To find the probability of all four bulbs being defective, we can use the multiplication rule of probability for independent events. The probability of the first bulb being defective is 0.05, the probability of the second bulb being defective given that the first bulb is already defective is also 0.05, and so on for the third and fourth bulbs. Therefore, the probability of all four bulbs being defective is:
0.05 x 0.05 x 0.05 x 0.05 = 0.00000625
Rounding this to eight decimal places gives us the answer of 0.00000625, which corresponds to choice D.

Question 10

Assuming there are 365 different birthdays, find the probability that five people chosen at random will have different birthdays. Round your answer to five decimal places. ​
A)0.97736
B)0.84986
C)0.87286
D)0.48643
E)0.97286

Accepted Answer

The probability that five people have different birthdays can be calculated by considering the fraction of the total number of ways their birthdays can be different to the total number of possible birthday combinations. For the first person, there are 365 choices out of 365. For the second person, to avoid the first person's birthday, there are 364 choices out of 365, and so on. Thus, the probability is (365/365) * (364/365) * (363/365) * (362/365) * (361/365) ≈ 0.97286.

Question 11

From a deck of 52 playing cards, two cards are drawn, one after the other without replacement. What is the probability that the first will be a king and the second will be a jack of the same suit? ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of From a deck of 52 playing cards,...

Question 12

A red ball and 10 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting 2 white W balls? ​
A)  
B) 
1
C)  
D)  
E)

Accepted Answer

The answer of A red ball and 10 white balls...

Question 13

Each computer component that the Peggos Company produces is tested twice before it is shipped. There is a 0.7 probability that a defective component will be so identified by the first test and a 0.8 probability that it will be identified as being defective by the second test. What is the probability that a defective component will not be identified as defective before it is shipped? ​
A)Pr(not identified) = 0.560
B)Pr(not identified) = 0.100
C)Pr(not identified) = 0.060
D)Pr(not identified) = 0.500
E)Pr(not identified) = 0.240

Accepted Answer

The probability that a defective component is identified by the first test is 0.7, so the probability that it is not identified by the first test is 0.3. If the component is not identified by the first test, it undergoes a second test. The probability that a defective component is identified by the second test is 0.8. Therefore, the probability that a defective component is not identified by either test is:
Pr(not identified) = (0.3)(0.2) = 0.06
So, the best answer is C.

Question 14

A box contains 7 red balls, 6 white balls, and 3 black balls. Two balls are drawn at random from the box without replacement of the first before the second is drawn. What is the probability of getting a red R ball on the first draw and a white W ball on the second? ​
A)Pr(R first ∩ W second) = 
B)Pr(R first ∩ W second) = 
C)Pr(R first ∩ W second) = 
D)Pr(R first ∩ W second) = 
E)Pr(R first ∩ W second) =

Accepted Answer

The answer of A box contains 7 red balls, 6...

Question 15

Thirty-seven percent of the cars owned by a car rental firm have some defect. What is the probability that if 3 cars are selected at random, at least one would have a defect? Round your answer to four decimal places. ​
A)0.0507
B)0.2500
C)0.7500
D)0.6031
E)0.8425

Accepted Answer

The answer of Thirty-seven percent of the cars owned by...

Question 16

An unprepared student must take a 7-question, multiple-choice test that has 5 possible answers per question. If the student can eliminate two of the possible answers on the first five questions, and if she guesses on every question, what is the probability that she will answer at least one question correctly? ​
A)Pr(at least 1 correct) = 
B)Pr(at least 1 correct) = 
C)Pr(at least 1 correct) = 
D)Pr(at least 1 correct) = 
E)Pr(at least 1 correct) =

Accepted Answer

The answer of An unprepared student must take a 7-question,...

Question 17

A company estimates that 50% of the country has seen its commercial and that if a person sees its commercial, there is a 45% probability that the person will buy its product. What is the probability that a person chosen at random in the country will have seen the commercial and bought the product? Round your answer to four decimal places. ​
A)0.0111
B)0.0500
C)0.4500
D)0.5000
E)0.2250

Accepted Answer

The probability that a person has seen the commercial is 0.5.
The probability that a person who has seen the commercial will buy the product is 0.45.
Therefore, the probability that a person chosen at random in the country will have seen the commercial and bought the product is:

P(seen commercial and bought product) = P(seen commercial) * P(bought product|seen commercial)
= 0.5 * 0.45
= 0.225

Therefore, the best choice is E.

Question 18

A red ball and 17 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting 2 red R balls? ​
A)Pr(R first ∩ R second) = 1
B)Pr(R first ∩ R second) = 
C)Pr(R first ∩ R second) = 
D)Pr(R first ∩ R second) = 
E)Pr(R first ∩ R second) = 0

Accepted Answer

The answer of A red ball and 17 white balls...

Question 19

From a deck of 52 playing cards, two cards are drawn, one after the other without replacement. What is the probability that the first will be an ace nd the second will be an ace? ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of From a deck of 52 playing cards,...

Question 20

An unprepared student must take a 7-question, multiple-choice test that has 5 possible answers per question. If the student can eliminate 2 of the possible answers on the first 4 questions, and if she guesses on every question, what is the probability that she will answer every question correctly? ​
A)Pr(all correct) = 
B)Pr(all correct) = 
C)Pr(all correct) = 
D)Pr(all correct) = 
E)Pr(all correct) =

Accepted Answer

Since the student can eliminate 2 out of 5 possible answers on the first 4 questions, she now has a 1 in 3 chance of guessing correctly on each of those questions. For the remaining 3 questions, she has a 1 in 5 chance of guessing correctly. Therefore, the probability of answering all 7 questions correctly would be (1/3)^4 * (1/5)^3, which simplifies to approximately 0.0000803. This matches Option B.

Quiz 8: Introduction to Probability

A red ball and 19 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting a red R ball on the first draw and a white W ball on the second?

Forty-eight percent of the U.S. population is female, and 23.3% of the female population have a college degree. If a U.S. resident is chosen at random, what is the probability, to three decimal places, that the person is a female with a college degree?

An unprepared student must take a 7-question, multiple-choice test that has 5 possible answers per question. If the student can eliminate 1 of the possible answers on the first 5 questions, and if she guesses on every question, what is the probability that she will answer every question incorrectly?

A bag contains 3 nickels, 5 dimes, and 4 quarters. If you draw 3 coins at random from the bag, without replacement, what is the probability that you will get a nickel N, a quarter Q, and a nickel N, in that order?

Two balls are drawn, without replacement, from a bag containing 18 blue balls numbered 1-18 and 4 green balls numbered 19-22. What is the probability that the first ball is blue and even-numbered and the second ball is even-numbered?

Suppose the following table summarizes the opinions of various groups on the issue of increased military spending. Given that a randomly selected individual is nonwhite NW, find the probability that he or she opposes increased military spending O.

If 5% of all light bulbs a company manufactures are defective, the probability of any one bulb being defective is 0.05. What is the probability that four bulbs drawn independently from the company's stock will be defective? Round your answer to eight decimal places.

Assuming there are 365 different birthdays, find the probability that five people chosen at random will have different birthdays. Round your answer to five decimal places.

From a deck of 52 playing cards, two cards are drawn, one after the other without replacement. What is the probability that the first will be a king and the second will be a jack of the same suit?

A red ball and 10 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting 2 white W balls?

A box contains 7 red balls, 6 white balls, and 3 black balls. Two balls are drawn at random from the box without replacement of the first before the second is drawn. What is the probability of getting a red R ball on the first draw and a white W ball on the second?

Thirty-seven percent of the cars owned by a car rental firm have some defect. What is the probability that if 3 cars are selected at random, at least one would have a defect? Round your answer to four decimal places.

A red ball and 17 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting 2 red R balls?

From a deck of 52 playing cards, two cards are drawn, one after the other without replacement. What is the probability that the first will be an ace nd the second will be an ace?

An unprepared student must take a 7-question, multiple-choice test that has 5 possible answers per question. If the student can eliminate 2 of the possible answers on the first 4 questions, and if she guesses on every question, what is the probability that she will answer every question correctly?

Quiz 8: Introduction to Probability

A red ball and 19 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting a red R ball on the first draw and a white W ball on the second? ​

Forty-eight percent of the U.S. population is female, and 23.3% of the female population have a college degree. If a U.S. resident is chosen at random, what is the probability, to three decimal places, that the person is a female with a college degree? ​

A bag contains 3 nickels, 5 dimes, and 4 quarters. If you draw 3 coins at random from the bag, without replacement, what is the probability that you will get a nickel N, a quarter Q, and a nickel N, in that order? ​

Two balls are drawn, without replacement, from a bag containing 18 blue balls numbered 1-18 and 4 green balls numbered 19-22. What is the probability that the first ball is blue and even-numbered and the second ball is even-numbered? ​

Suppose the following table summarizes the opinions of various groups on the issue of increased military spending. ​ ​ Given that a randomly selected individual is nonwhite NW, find the probability that he or she opposes increased military spending O. ​

If 5% of all light bulbs a company manufactures are defective, the probability of any one bulb being defective is 0.05. What is the probability that four bulbs drawn independently from the company's stock will be defective? Round your answer to eight decimal places. ​

Assuming there are 365 different birthdays, find the probability that five people chosen at random will have different birthdays. Round your answer to five decimal places. ​

From a deck of 52 playing cards, two cards are drawn, one after the other without replacement. What is the probability that the first will be a king and the second will be a jack of the same suit? ​

A red ball and 10 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting 2 white W balls? ​

A box contains 7 red balls, 6 white balls, and 3 black balls. Two balls are drawn at random from the box without replacement of the first before the second is drawn. What is the probability of getting a red R ball on the first draw and a white W ball on the second? ​

Thirty-seven percent of the cars owned by a car rental firm have some defect. What is the probability that if 3 cars are selected at random, at least one would have a defect? Round your answer to four decimal places. ​

A red ball and 17 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting 2 red R balls? ​

From a deck of 52 playing cards, two cards are drawn, one after the other without replacement. What is the probability that the first will be an ace nd the second will be an ace? ​