Q: A card is drawn at random from a standard deck of 52 cards. What is the probability that the card is either a queen or a black card?

$$P(\text{Queen or Black}) = \frac{15}{26}$$

Q: A card is drawn from a standard deck. What is the probability that the card is a face card or a heart?

$$P(\text{Face or Heart}) = \frac{22}{52}$$

Question 1

Which of the following is the correct formula for the probability of the union of two events A and B that are not mutually exclusive?

Accepted Answer

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

Question 2

A card is drawn at random from a standard deck of 52 cards. What is the probability that the card is either a queen or a black card?

Accepted Answer

$$P(	ext{Queen or Black}) = \frac{15}{26}$$

Question 3

Which of the following statements about discrete probability distributions is TRUE?

Accepted Answer

The sum of all probabilities in a discrete probability distribution must equal 1.

Question 4

In a binomial experiment with $$n$$ trials, what does the random variable $$X$$ measure?

Accepted Answer

The number of successes in $$n$$ trials.

Question 5

If the odds of an event $$E$$ are $$7:2$$, what is $$P(E)$$?

Accepted Answer

$$P(E) = \frac{7}{9}$$

Question 6

A six-sided die is rolled 80 times. If the probability of rolling a 1 is $$0.15$$, a 2 is $$0.25$$, a 3 is $$0.10$$, a 4 is $$0.10$$, a 5 is $$0.20$$, and a 6 is $$0.20$$, is this a probability distribution?

Accepted Answer

Yes, because all probabilities are between 0 and 1 and sum to 1.

Question 7

Which formula gives the variance of a discrete probability distribution?

Accepted Answer

$$\$$sigma^2$$ = \sum (x - \mu)^2$ P(x)$$

Question 8

A binomial experiment has $$n = 10$$ and $$p = 0.3. $$What is the expected value (mean) of the number of successes?

Accepted Answer

$$\mu = 3$$

Question 9

If two events $$A$$ and $$B$$ are independent, which formula correctly gives $$P(A \cap B)$$?

Accepted Answer

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

Question 10

A smartphone manufacturer receives a shipment of 5000 batteries. If the probability that a battery is defective is $$0.05$$, what is the expected number of defective batteries in the shipment?

Accepted Answer

$$250$$

Question 11

Which of the following is NOT a condition for a discrete probability distribution?

Accepted Answer

Each probability must be greater than 1.

Question 12

In a binomial experiment, what does it mean for each trial to be independent?

Accepted Answer

The outcome of one trial does not affect the outcome of any other trial.

Question 13

A card is drawn from a standard deck. What is the probability that the card is a face card or a heart?

Accepted Answer

$$P(	ext{Face or Heart}) = \frac{22}{52}$$

Question 14

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

Accepted Answer

$$0.7$$

Question 15

Which of the following is a TRUE statement about the mean of a probability distribution?

Accepted Answer

It represents the long-run average value of the random variable.

Question 16

A roulette player plays 8 games, each with a probability of winning $$0.4734. $$What is the probability that the player wins more than 2 games? (Use the binomial formula.)

Accepted Answer

$$1 - \sum_{r=0}^{2} \left( \begin{array}{c} 8 \ r \end{array} ight) (0.4734)^r (0.5266$$)^{8-r}$$

Question 17

If two cards are drawn in succession without replacement from a standard deck, what is the probability that both cards are black?

Accepted Answer

$$\frac{26}{52} 	imes \frac{25}{51}$$

Question 18

Which of the following is the correct formula for the probability of $$r$$ successes in $$n$$ binomial trials with probability $$p of $$success?

Accepted Answer

$$P(r) = \left( \begin{array}{c} n \ r \end{array} ight) p^r q$$^{n-r}$$

Introductory Statistics Practice Exam 2 Study Guide

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