Q: If two events $$A$$ and $$B$$ are independent, which of the following is true?

$$P(A \cap B) = P(A) \times P(B)$$

Q: A factory has three machines: I, II, and III, producing 35%, 25%, and 40% of springs, respectively. Their defect rates are 2%, 1%, and 3%. What is the probability that a randomly selected spring is defective?

$$0.02 \times 0.35 + 0.01 \times 0.25 + 0.03 \times 0.40 = 0.0205$$

Question 1

Which of the following best describes a random phenomenon in probability?

Accepted Answer

A process where the set of possible outcomes is known, but the specific outcome cannot be predicted with certainty.

Question 2

Suppose you flip three fair coins. What is the probability that all three coins show the same face?

Accepted Answer

$$\frac{1}{4}$$

Question 3

Which of the following is an example of a deterministic phenomenon?

Accepted Answer

Today's date.

Question 4

If you observe that you get stopped at a train track 6 times out of 40 days, what is the empirical probability of getting stopped?

Accepted Answer

$$\frac{6}{40}$$

Question 5

Which statement about the Law of Large Numbers is correct?

Accepted Answer

It states that as the number of trials increases, the empirical probability approaches the theoretical probability.

Question 6

A president and a vice president are chosen from a class of 6 males and 4 females. What is the probability that they are of opposite genders?

Accepted Answer

$$\frac{48}{90}$$

Question 7

Which formula correctly gives the number of permutations of $$n$$ objects taken $$k at a $$time (without replacement)?

Accepted Answer

$$\frac{n!}{(n-k)!}$$

Question 8

You want to borrow 3 books from a collection of 5. How many ways can you choose the books if order does not matter?

Accepted Answer

$$10$$

Question 9

Which of the following is the correct formula for the probability of the union of two events $$A$$ and $$B$$?

Accepted Answer

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

Question 10

If events $$A$$ and $$B$$ are disjoint, which of the following is true?

Accepted Answer

$$P(A \cap B) = 0$$

Question 11

A drawer contains 4 blue, 5 gray, and 3 black socks. If you randomly select two socks, what is the probability that both are blue?

Accepted Answer

$$\frac{1}{22}$$

Question 12

Which of the following is NOT a valid probability axiom?

Accepted Answer

For any event $$A$$, $$P(A) \u003c 0.$$

Question 13

If $$P(A) = 0.3$$, what is $$P(A^c)$$, the probability of the complement of $$A$$?

Accepted Answer

$$0.7$$

Question 14

Forty-five percent of Americans like to cook, 59% like to shop, and 23% enjoy both. What is the probability that a randomly chosen American enjoys either cooking or shopping or both?

Accepted Answer

$$0.81$$

Question 15

Which of the following best describes conditional probability?

Accepted Answer

The probability of an event occurring given that another event has occurred.

Question 16

Given $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.2$$, what is $$P(A \cup B)$$?

Accepted Answer

$$0.7$$

Question 17

If two events $$A$$ and $$B$$ are independent, which of the following is true?

Accepted Answer

$$P(A \cap B) = P(A) 	imes P(B)$$

Question 18

A factory has three machines: I, II, and III, producing 35%, 25%, and 40% of springs, respectively. Their defect rates are 2%, 1%, and 3%. What is the probability that a randomly selected spring is defective?

Accepted Answer

$$0.02 	imes 0.35 + 0.01 	imes 0.25 + 0.03 	imes 0.40 = 0.0205$$

Question 19

Which of the following is the correct expression for the number of combinations of $$n$$ objects taken $$k at a $$time?

Accepted Answer

$$\frac{n!}{k!(n-k)!}$$

Probability: Foundations, Rules, and Applications (Chapter 12 Study Notes)

Guida di studio - Domande di pratica

Study guide - Flashcard