Question 1

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 2

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 3

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 4

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 5

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

Using the law of total probability, we have:

P(bought) = P(bought | seen)P(seen) + P(bought | not seen)P(not seen)
P(bought) = (0.45)(0.5) + (0)(0.5)
P(bought) = 0.225

Therefore, the probability that a person chosen at random in the country will have seen the commercial and bought the product is 0.225.

Question 6

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

There are 4 kings and 4 jacks in a deck of playing cards. Since the question specifies that the jack must be of the same suit as the king drawn, there are only 1 jack of the same suit remaining after drawing a king. Therefore, the probability of drawing a king as the first card is 4/52 (or 1/13) and the probability of drawing the matching jack as the second card is 1/51 (since there is one less card in the deck). The probabilities of these two events happening together is the product of their individual probabilities, which is (4/52) * (1/51) = 1/663.

Question 7

Suppose the following table summarizes the opinions of various groups on the issue of increased military spending. ​

Accepted Answer

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

Question 8

A red ball and 18 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting 2 white W balls? ​
A) Pr(W first ∩ W second) = 
B) Pr(W first ∩ W second) = 1
C) Pr(W first ∩ W second) = 
D) Pr(W first ∩ W second) = 
E) Pr(W first ∩ W second) =

Accepted Answer

There are 18 white balls and 19 total balls in the box. So, the probability of drawing a white ball on the first draw is 18/19. Since we are not replacing the first ball before drawing the second one, there are now 17 white balls and 18 total balls left in the box. So, the probability of drawing a white ball on the second draw, given that the first ball was white, is now 17/18. Therefore, the probability of getting two white balls in a row is (18/19) x (17/18) = 306/342 = 0.895 or approximately 0.896. Therefore, the answer is C.

Question 9

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

Since there is only one red ball in the box and two balls are drawn without replacement, the probability of getting two red balls is zero.

Question 10

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 11

A box contains 3 red balls, 5 white balls, and 3 black balls. Two balls are drawn at random from the box with 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 3 red balls, 5...

Question 12

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 13

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 of a U.S. resident being a female with a college degree, we need to find the intersection of the two events: female and college degree. 
Probability of being female = 48/100 = 0.48 
Probability of having a college degree given the person is female = 23.3/100 = 0.233

So, 
Pr(female ∩ college degree) = Pr(college degree | female) x Pr(female) 
= 0.233 x 0.48 
= 0.11184 
Rounding off to three decimal places, we get 0.112, which corresponds to option D.

Question 14

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

If a defective component is not identified by the first or second test, then it will not be shipped. The probability of a defective component not being identified by the first test is 1 - 0.7 = 0.3. The probability of a defective component not being identified by either test is the product of the probabilities: 0.3 * 0.2 = 0.06 or 6%. Therefore, the probability that a defective component will not be identified as defective before it is shipped is 0.06 or 6%. The correct choice is C.

Question 15

A fair die is thrown twice. What is the probability that a 3 will result the first time and a 2 the second time? ​
A) Pr(3 first ∩ 2 second) = 
B) Pr(3 first ∩ 2 second) = 
C) Pr(3 first ∩ 2 second) = 
D) Pr(3 first ∩ 2 second) = 
E) Pr(3 first ∩ 2 second) =

Accepted Answer

The answer of A fair die is thrown twice. What...

Question 16

The following table gives the results of a 2005 survey of 1000 people regarding the funding of universal health care by employers (employer mandate). ​

Accepted Answer

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

Question 17

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 18

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 19

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

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

Question 20

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 two bulbs drawn independently from the company's stock will be defective? Round your answer to eight decimal places. ​
A) 0.25000000
B) 0.00012500
C) 0.05000000
D) 0.00250000
E) 0.00000000

Accepted Answer

The probability of drawing two defective bulbs can be calculated using the formula for independent events:

P(A and B) = P(A) x P(B)

where A and B are the events of drawing a defective bulb.

Therefore:

P(two defective bulbs) = P(A and B) 
= P(A) x P(B) 
= 0.05 x 0.05 
= 0.0025

Rounding to eight decimal places gives us 0.00250000, which matches choice D.

Quiz 7: Introduction to Probability

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 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 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?

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?

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?

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 red ball and 18 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting 2 white W balls?

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 box contains 3 red balls, 5 white balls, and 3 black balls. Two balls are drawn at random from the box with 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.

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 fair die is thrown twice. What is the probability that a 3 will result the first time and a 2 the second time?

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?

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?

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?

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 two bulbs drawn independently from the company's stock will be defective? Round your answer to eight decimal places.

Quiz 7: Introduction to Probability

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 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 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? ​

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? ​

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? ​

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 red ball and 18 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting 2 white W balls? ​

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 box contains 3 red balls, 5 white balls, and 3 black balls. Two balls are drawn at random from the box with 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. ​

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 fair die is thrown twice. What is the probability that a 3 will result the first time and a 2 the second time? ​

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? ​

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 two bulbs drawn independently from the company's stock will be defective? Round your answer to eight decimal places. ​