Q: If two events A and B are independent, which formula correctly gives the probability that both A and B occur?

$$P(A \text{ and } B) = P(A) \times P(B)$$

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?

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

Question 1

Which of the following best describes a simple event in probability?

Accepted Answer

An outcome or event that cannot be further broken down into simpler components.

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

Which of the following is an example of using the classical approach to probability?

Accepted Answer

Calculating the probability of drawing an ace from a standard deck of cards.

Question 5

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

Accepted Answer

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

Question 6

Which of the following statements about the Law of Large Numbers is correct?

Accepted Answer

It states that as a procedure is repeated, the relative frequency probability approaches the actual probability.

Question 7

If two events A and B are independent, which formula correctly gives the probability that both A and B occur?

Accepted Answer

$$P(A 	ext{ and } B) = P(A) 	imes P(B)$$

Question 8

A card is drawn from a deck and replaced, then a second card is drawn. What is the probability of getting a queen and then an ace?

Accepted Answer

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

Question 9

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

$$\frac{4}{100} = \frac{1}{25}$$

Question 10

Which of the following best describes disjoint (mutually exclusive) events?

Accepted Answer

Events that cannot occur at the same time.

Question 11

If $$P(A) = 0.3$$, $$P(B) = 0.4$$, and $$A$$ and $$B$$ are disjoint, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.7$$

Question 12

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 13

A factory produces products with 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 14

Which formula gives the conditional probability of event B given event A?

Accepted Answer

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

Question 15

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

Accepted Answer

$$6^4$$

Question 16

A football team consists of 20 freshmen, 20 sophomores, 15 juniors, and 10 seniors. Four players are selected at random. What is the probability that all four are seniors?

Accepted Answer

$$\frac{\binom{10}{4}}{\binom{65}{4}}$$

Question 17

If a coin is flipped and a die is rolled, how many possible outcomes are there for the sequence of events?

Accepted Answer

$$2 	imes 6 = 12$$

Question 18

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

Accepted Answer

If an observed event has a probability less than or equal to 0.05 under a given assumption, we question the assumption.

Chapter 4: Introduction to Probability – Structured Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard