Chapter 5 MCQ Practice #1

Which of the following pairs of events are disjoint (mutually exclusive)?

1. event A: the numbers less than 4; event B: all negative numbers

2. event A: the odd numbers; event B: the number 5

3. event A: the even numbers; event B: the numbers greater than 10

4. event A: the numbers above 100; event B: the numbers less than -200

5. event A: negative numbers; event B: odd numbers

4. event A: the numbers above 100; event B: the numbers less than -200

Government data show that 26% of the civilian labor force has at least 4 years of college and that 15% of the labor force works as laborers or operators of machines or vehicles. Can you conclude that because (0.26)(0.15) = 0.039 about 4% of the labor force are college-educated laborers or operators?

1. No, because the events are not mutually exclusive

2. No, because the events are not independent

3. Yes, by the mulitplication rule

4. Yes, by the law of large numbers

5. Yes, by conditional probabilities

2. No, because the events are not independent

You play tennis regularly with a friend, and from past experience, you believe that the outcome of each match is independent. For any given match you have a probability of 0.6 of winning. The probability you win the next two matches is

1. 0.16

2. 1.2

3. 0.6

4. 0.36

5. 0.4

4. 0.36

If P(A) = 0.24 and P(B) = 0.52 and A and B are independent, what is P(A or B)?

1. 0.28

2. the answer cannot be determined from the information given

3. 0.76

4. 0.1248

5. 0.6352

5. 0.6352

If A U B = S (sample space), and P(A U B^c) = 0.25, and P(A^c) = 0.35, then P(B) =

1. 0.35

2. 0.4

3. 0.75

4. None of these

5. 0.65

3. 0.75

Melissa is looking for the perfect man. She claims that of the men at her college, 41% are smart, 32% are funny, and 20% are both smart and funny. If Melissa is right, what is the probability that a man chosen at random from her college is neither funny nor smart?

1. 0.8

2. 0.67

3. 0.47

4. 0.27

5. 0.0

4. 0.47

An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1.

The conditional probability of A given B is

1. cannot be determined from the information given

2. 0.3

3. 0.2

4. 0.5

5. 1/6

5. 1/6

An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1.

We may conclude that

1. none of these

2. either A or B always occurs.

3. events A and B are disjoint.

4. events A and B are independent.

5. events A and B are complementary.

2. either A or B always occurs.

Experience has shown that a certain lie detector will show a positive reading (indicate a lie) 10% of the time when a person is telling the truth and 95% of the time when a person is lying. Suppose that a random sample of 5 suspects is subjected to a lie detector test regarding a recent one-person crime. Then the probability of observing no positive reading if all suspects plead innocent and are telling the truth is

1. 0.99999

2. 0.591

3. 0.00001

4. 0.409

5. 0.735

2. 0.591

A box contains 12 batteries of which 6 are still working. Anne starts picking batteries one at a time from the box and testing them. Find the probability that she has to pick 5 batteries in order to find one that works.

1. 0.031

2. 0.008

3. 0.675

4. 0.009

5. 0.023

5. 0.023

A single fair die is rolled, find the probability of a 5 given that the number rolled is odd.

1. 2/3

2. 1.0

3. 1/6

4. 1/3

5. 1/2

4. 1/3

If you buy one ticket in the Provincial Lottery, then the probability that you will win a prize is 0.11. If you buy one ticket each month for five months, what is the probability that you will win at least one prize?

1. 0.50

2. 0.44

3. 0.45

4. 0.55

5. 0.56

2. 0.44

Event A occurs with probability 0.2. Event B occurs with probability 0.8. If A and B are disjoint (mutually exclusive), then

1. both P(A and B) = 0.16 and P(A or B) = 1.0 are true

2. P(A or B) = 1.0

3. P(A or B) = 0.16

4. P(A and B) = 0.16

5. P(A and B) = 1.0

2. P(A or B) = 1.0

A fair coin is tossed four times, and each time the coin lands heads up. If the coin is then tossed 1996 more times, how many heads are most likely to appear for these 1996 additional tosses?

1. 998

2. 1996

3. 996

4. none of these

5. 1000

1. 998

At Sally's Hair Salon there are three hair stylists.

21% of the hair cuts are done by Chris, 31% are done by Karine, and 48% are done by Amy.

Chris finds that when he does haircuts, 7% of the customers are not satisfied.

Karine finds that when she does haircuts, 8% of the customers are not satisfied.

Amy finds that when she does haircuts, 5% of the customers are not satisfied.

What percentage of unhappy customers had their hair cut by Amy?

1. 48%

2. 23.1%

3. 60.8%

4. 5%

5. 37.8%

5. 37.8%

The table below describes the smoking habits of a group of asthma sufferers. Is heavy smoking indpendent of gender?

	Non-smoker	Light smoker	Heavy smoker	Total
Men	304	67	88	459
Women	330	89	61	480
Total	634	156	149	939

 

1. Yes, the percentage of women in each smoking category is the same as the percentage of men in each smoking category.

2. Yes, a heavy smoker cannot be both a man and a woman.

3. No, P(male and heavy smoker) = 0.094; P(female and heavy smoker) = 0.065; These are not equal.

4. Yes, because each of the joint probabilities is equal to the product of the marginal probabilities.

5. No, overall 15.9% of the group are heavy smokers, but 19.2% of the men are heavy smokers. These are not equal.

5. No, overall 15.9% of the group are heavy smokers, but 19.2% of the men are heavy smokers. These are not equal.