Q: A committee of 3 women and 2 men is to be chosen from 7 women and 5 men. How many different possibilities are there?

$$\binom{7}{3} \times \binom{5}{2}$$

Q: A radio talk host can select 3 of 6 special guests for her program. The order of appearance is important. How many ways can this be done?

$$P(6,3) = 6 \times 5 \times 4 = 120$$

Q: A store has 6 TV magazines and 8 news magazines. If two customers each buy one magazine, what is the probability that one buys a TV magazine and the other buys a news magazine (without replacement)?

$$\frac{6}{14} \times \frac{8}{13} + \frac{8}{14} \times \frac{6}{13}$$

Q: A deck of cards is shuffled and two cards are drawn without replacement. What is the probability that the first card is a queen and the second card is an ace?

$$\frac{4}{52} \times \frac{4}{51}$$

Question 1

Which of the following best describes the Law of Large Numbers?

Accepted Answer

As the number of trials increases, the relative frequency probability of an event tends to approach the actual probability.

Question 2

A family has three children. What is the probability that exactly two of them are boys, assuming each child is equally likely to be a boy or a girl?

Accepted Answer

$$\frac{3}{8}$$

Question 3

If a die is rolled, what is the probability of NOT getting a 3?

Accepted Answer

$$\frac{5}{6}$$

Question 4

A survey of 2003 adults found that 366 said they have seen or been in the presence of a ghost. What is the probability that a randomly selected adult from this survey answered 'yes'?

Accepted Answer

$$\frac{366}{2003}$$

Question 5

Which of the following is an example of a subjective probability?

Accepted Answer

Estimating the probability of rain tomorrow based on weather patterns and personal experience.

Question 6

A coin is flipped and a die is rolled. What is the probability of getting a head on the coin and a 4 on the die?

Accepted Answer

$$\frac{1}{12}$$

Question 7

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

Accepted Answer

Selecting a person who is a male and selecting a person who is a female.

Question 8

A box contains 3 red marbles, 5 green marbles, and 2 blue marbles. If a marble is selected, replaced, and then a second marble is selected, what is the probability of selecting a blue marble both times?

Accepted Answer

$$\frac{1}{25}$$

Question 9

If two cards are drawn from a standard deck of 52 cards without replacement, what is the probability that both are aces?

Accepted Answer

$$\frac{4}{663}$$

Question 10

A committee of 3 women and 2 men is to be chosen from 7 women and 5 men. How many different possibilities are there?

Accepted Answer

$$\binom{7}{3} 	imes \binom{5}{2}$$

Question 11

A radio talk host can select 3 of 6 special guests for her program. The order of appearance is important. How many ways can this be done?

Accepted Answer

$$P(6,3) = 6 	imes 5 	imes 4 = 120$$

Question 12

If the probability of a defective product is 0.15, what is the probability that in a sample of 12 products, at least one is defective?

Accepted Answer

$$1 - (0.85$$)^{12}$$

Question 13

Which formula correctly expresses the conditional probability of event B given event A?

Accepted Answer

$$P(B|A) = \frac{P(A \cap B)}{P(A)}$$

Question 14

A store has 6 TV magazines and 8 news magazines. If two customers each buy one magazine, what is the probability that one buys a TV magazine and the other buys a news magazine (without replacement)?

Accepted Answer

$$\frac{6}{14} 	imes \frac{8}{13} + \frac{8}{14} 	imes \frac{6}{13}$$

Question 15

Which of the following is NOT a requirement for using the classical approach to probability?

Accepted Answer

The experiment must be repeatable.

Question 16

If a year is selected at random, what is the probability that Thanksgiving Day in the United States will be on a Thursday?

Accepted Answer

1

Question 17

A deck of cards is shuffled and two cards are drawn without replacement. What is the probability that the first card is a queen and the second card is an ace?

Accepted Answer

$$\frac{4}{52} 	imes \frac{4}{51}$$

Question 18

Which of the following best describes the complement of an event A?

Accepted Answer

All outcomes in the sample space that are not in event A.

Question 19

A mountain has 4 ways to go up and 4 ways to go down. In how many ways can you go up and down if you cannot use the same way both times?

Accepted Answer

12

Chapter 4: Introduction to Probability – Structured Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard