Question 1

Given the following probability distribution for the number of heads in two coin tosses: $$P(0) = 0.25$$, $$P(1) = 0.5$$, $$P(2) = 0.25. $$What is the expected value of the number of heads?

Accepted Answer

$$E(X) = 1$$

Question 2

A student randomly guesses on a 4-question true/false quiz. What is the probability that the student gets exactly 2 questions correct?

Accepted Answer

$$P = 0.375$$

Question 3

If a fair die is rolled twice, what is the probability that the sum is 7?

Accepted Answer

$$P = \frac{1}{6}$$

Question 4

A bag contains 3 red, 2 blue, and 5 green marbles. If one marble is drawn at random, what is the probability it is not green?

Accepted Answer

$$P = 0.5$$

Question 5

Which of the following is the correct formula for the expected value $$E(X) of a $$discrete random variable $$X$$ with possible values $$x_i$$ and probabilities $$P(x_i)$$?

Accepted Answer

$$E(X) = \sum x_i P(x_i)$$

Question 6

If the probability of event $$A is$$ $$0.3$$ and the probability of event $$B is$$ $$0.4$$, and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$P(A \cup B) = 0.7$$

Question 7

A multiple-choice question has 5 possible answers, only one of which is correct. If a student guesses, what is the probability of getting the question wrong?

Accepted Answer

$$P = 0.8$$

Question 8

If $$P(A) = 0.6$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.3$$, what is $$P(A \cup B)$$?

Accepted Answer

$$P(A \cup B) = 0.8$$

Question 9

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

Accepted Answer

$$P = 0.25$$

Question 10

If a card is drawn at random from a standard deck of 52 cards, what is the probability that it is a heart or a king?

Accepted Answer

$$P = \frac{16}{52}$$

Question 11

A fair coin is tossed three times. What is the probability of getting exactly two heads?

Accepted Answer

$$P = 0.375$$

Question 12

Which of the following best describes a mutually exclusive event?

Accepted Answer

Two events that cannot occur at the same time

Question 13

If $$P(A) = 0.4$$ and $$P(B|A) = 0.5$$, what is $$P(A \cap B)$$?

Accepted Answer

$$P(A \cap B) = 0.2$$

Question 14

A box contains 4 white balls and 6 black balls. If two balls are drawn at random without replacement, what is the probability that both are black?

Accepted Answer

$$P = \frac{1}{3}$$

Question 15

If the probability of rain on any given day is $$0.3$$, what is the probability that it does not rain on two consecutive days?

Accepted Answer

$$P = 0.49$$

Question 16

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

Accepted Answer

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

Counting & Probability: Liberal Arts Math Study Notes

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