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 deck of 52 cards: What is the probability of drawing 3 jacks in a row without replacement?

$$\frac{4}{52} \times \frac{3}{51} \times \frac{2}{50}$$

Q: A store has 6 TV magazines and 8 news magazines. If two customers each buy one magazine, what is the probability that one of each type is purchased?

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

Question 1

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 and the order matters?

Accepted Answer

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

Question 2

A die is rolled once. What is the probability of NOT getting a 3?

Accepted Answer

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

Question 3

In a survey, 366 adults said 'yes' and 1637 said 'no' to seeing a ghost. What is the probability that a randomly selected adult said 'yes'?

Accepted Answer

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

Question 4

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 approaches the actual probability.

Question 5

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 6

If two cards are drawn from a deck with replacement, what is the probability of drawing a queen first and an ace second?

Accepted Answer

$$\frac{1}{169}$$

Question 7

A box contains 3 red, 5 green, and 2 blue marbles. If two marbles are drawn with replacement, what is the probability both are blue?

Accepted Answer

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

Question 8

Which of the following is an example of disjoint (mutually exclusive) events?

Accepted Answer

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

Question 9

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 10

If a student guesses on a 5-question multiple choice test with 4 options each, what is the probability of getting all 5 correct?

Accepted Answer

$$\left(\frac{1}{4}\$$right)^5$$

Question 11

A factory has a defect rate of 15%. If a customer buys 12 products, what is the probability that at least one is defective?

Accepted Answer

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

Question 12

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 13

How many different 4-letter code words can be made from the letters in the word PENCIL if repetitions are permitted?

Accepted Answer

$$6^4$$

Question 14

A deck of 52 cards: What is the probability of drawing 3 jacks in a row without replacement?

Accepted Answer

$$\frac{4}{52} 	imes \frac{3}{51} 	imes \frac{2}{50}$$

Question 15

A store has 6 TV magazines and 8 news magazines. If two customers each buy one magazine, what is the probability that one of each type is purchased?

Accepted Answer

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

Question 16

Which of the following is a classical approach to probability?

Accepted Answer

Assuming all outcomes are equally likely and using $$P(A) = \frac{s}{n}$$

Question 17

If the probability of an event is 0.001, how would you interpret this?

Accepted Answer

The event is very unlikely to occur.

Question 18

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 twice?

Accepted Answer

$$4 	imes 3 = 12$$

Question 19

Which of the following is a correct statement about the rare event rule for inferential statistics?

Accepted Answer

If an observed event is very unlikely under a given assumption, the assumption is probably not correct.

Chapter 4: Introduction to Probability – Structured Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard