Q: Which of the following statements is TRUE about disjoint (mutually exclusive) events?

If two events are disjoint, $$P(A \text{ and } B) = 0$$

Q: A bag contains 5 red, 3 blue, and 2 green marbles. If two marbles are drawn one after another without replacement, what is the probability that both are blue?

$$P = \frac{3}{10} \times \frac{2}{9}$$

Q: A lottery ticket costs $$2 and pays 100 if $$you win (probability 0.001), otherwise you win nothing. What is the expected value of buying one ticket?

$$E = (100-2) \times 0.001 + (-2) \times 0.999$$

Question 1

A hospital administrator wants to estimate the probability that a randomly selected patient will require an MRI scan. She reviews the records of the last 500 patients and finds that 40 required an MRI. Which type of probability is she using?

Accepted Answer

Empirical probability

Question 2

Which of the following sets of probabilities represents a valid probability model?

Accepted Answer

$$P(A) = 0.3$$, $$P(B) = 0.5$$, $$P(C) = 0.2$$

Question 3

A fair die is rolled. What is the probability of rolling an even number or a number greater than 4?

Accepted Answer

$$P(E) = \frac{4}{6}$$

Question 4

Which of the following statements is TRUE about disjoint (mutually exclusive) events?

Accepted Answer

If two events are disjoint, $$P(A 	ext{ and } B) = 0$$

Question 5

A bag contains 5 red, 3 blue, and 2 green marbles. If two marbles are drawn one after another without replacement, what is the probability that both are blue?

Accepted Answer

$$P = \frac{3}{10} 	imes \frac{2}{9}$$

Question 6

A student claims that the probability of rain tomorrow is 70% based on her intuition and experience. This is an example of:

Accepted Answer

Subjective probability

Question 7

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A 	ext{ and } B) = 0.2$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$P(A 	ext{ or } B) = 0.9$$

Question 8

A password consists of 3 letters followed by 2 digits. If letters and digits can be repeated, how many different passwords are possible?

Accepted Answer

$$26^3$$ 	imes $$10^2$$

Question 9

Which of the following random variables is continuous?

Accepted Answer

The time (in seconds) it takes for a chemical reaction to complete

Question 10

Given the following probability distribution for $$X$$: $$P(X=0)=0.2$$, $$P(X=1)=0.5$$, $$P(X=2)=0.3$$, what is the mean (expected value) of $$X$$?

Accepted Answer

$$E(X) = 1.1$$

Question 11

A lottery ticket costs $$2 and pays 100 if $$you win (probability 0.001), otherwise you win nothing. What is the expected value of buying one ticket?

Accepted Answer

$$E = (100-2) 	imes 0.001 + (-2) 	imes 0.999$$

Question 12

Which of the following is NOT a property of the normal distribution?

Accepted Answer

The area under the curve is less than 1

Question 13

For a normal distribution with mean $$\mu = 100$$ and standard deviation $$\sigma = 15$$, what is the $$z-$$score for $$x = 130$$?

Accepted Answer

$$z = 2$$

Question 14

If the area to the left of a $$z-$$score is 0.8413, what is the value of $$z$$?

Accepted Answer

$$z = 1$$

Question 15

Suppose the weights of apples are normally distributed with mean $$\mu = 150$$ grams and standard deviation $$\sigma = 20$$ grams. What is the probability that a randomly selected apple weighs more than 170 grams?

Accepted Answer

Find $$z = \frac{170-150}{20} = 1$$, then $$P(X \u003e 170) = 1 - 0.8413 = 0.1587$$

Question 16

If $$P(A) = 0.3$$, what is the probability that event $$A$$ does NOT occur?

Accepted Answer

$$P(A') = 0.7$$

Question 17

A committee of 4 is to be chosen from 10 people. How many different committees are possible?

Accepted Answer

$$\binom{10}{4}$$

Question 18

A survey finds that 60% of adults drink coffee, 30% drink tea, and 10% drink both. What is the probability that a randomly selected adult drinks coffee or tea?

Accepted Answer

$$P = 0.6 + 0.3 - 0.1 = 0.8$$

Question 19

If $$P(B|A) = 0.4$$ and $$P(A) = 0.5$$, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$P(A 	ext{ and } B) = 0.2$$

Question 20

Which of the following statements about the probability of a single, exact value for a continuous random variable is correct?

Accepted Answer

The probability is 0

Probability, Discrete and Continuous Probability Distributions, and the Normal Distribution: Study Guide

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