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

$$P(\text{queen or black}) = \frac{4}{52} + \frac{26}{52} - \frac{2}{52} = \frac{28}{52}$$

Q: A ball is drawn at random from an urn containing 8 red, 4 blue, and 3 green balls. What is the probability that the ball is red or green?

$$P(\text{red or green}) = \frac{8+3}{15} = \frac{11}{15}$$

Question 1

Which of the following is a condition that must be satisfied for a discrete probability distribution?

Accepted Answer

The sum of all probabilities must equal 1.

Question 2

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

Accepted Answer

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

Question 3

If 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 4

A card is selected at random from a standard deck. What is the probability that the card is either a queen or a black card?

Accepted Answer

$$P(	ext{queen or black}) = \frac{4}{52} + \frac{26}{52} - \frac{2}{52} = \frac{28}{52}$$

Question 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

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

No, because the probabilities do not sum to 1.

Question 8

In a binomial distribution with $$n = 10$$ and $$p = 0.52$$, what is the expected number of successes?

Accepted Answer

$$\mu = 10 	imes 0.52 = 5.2$$

Question 9

Which formula gives the variance of a binomial distribution?

Accepted Answer

$$\$$sigma^2$$ = npq$$

Question 10

A shipment of 5000 batteries has a 5% defect rate. What is the expected number of defective batteries?

Accepted Answer

$$5000 	imes 0.05 = 250$$

Question 11

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

Accepted Answer

$$P(A \cup B) = 0.4 + 0.5 - 0.2 = 0.7$$

Question 12

A ball is drawn at random from an urn containing 8 red, 4 blue, and 3 green balls. What is the probability that the ball is red or green?

Accepted Answer

$$P(	ext{red or green}) = \frac{8+3}{15} = \frac{11}{15}$$

Question 13

Which of the following is NOT a requirement for a binomial experiment?

Accepted Answer

The probability of success changes from trial to trial.

Question 14

If $$P(E) = 0.3$$, what is $$P(E^c)$$?

Accepted Answer

$$P(E^c) = 0.7$$

Question 15

In a probability distribution, what does the variance measure?

Accepted Answer

The spread of the outcomes around the mean.

Question 16

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

Accepted Answer

$$P(r \u003e 2) = 1 - \sum_{r=0}^{2} \left( \begin{array}{c} 8 \ r \end{array} ight) (0.4734)^r (0.5266$$)^{8-r}$$

Question 17

If a distribution is approximately symmetric and bell-shaped, about what percentage of the data will lie within two standard deviations of the mean?

Accepted Answer

About 95%

Question 18

Which of the following is the correct formula for the mean of a discrete probability distribution?

Accepted Answer

$$\mu = \sum x P(x)$$

Question 19

A standard deck of cards is used. What is the probability of drawing a jack that is red or a queen?

Accepted Answer

$$P(	ext{red jack or queen}) = \frac{2}{52} + \frac{4}{52} - \frac{0}{52} = \frac{6}{52}$$

Introductory Statistics Practice Exam 2 Study Guide

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