Question 1

A bag contains 3 red, 5 blue, and 2 green marbles. If one marble is drawn at random, what is the sample space for this experiment?

Accepted Answer

{Red, Blue, Green}

Question 2

If the probability of event $$A is$$ $$0.7$$, what is the probability of the complement of $$A$$ ($$\overline{A}$$)?

Accepted Answer

$$0.3$$

Question 3

Which of the following is NOT a valid probability value?

Accepted Answer

$$-0.2$$

Question 4

A fair six-sided die is rolled. What is the probability of rolling a number greater than 4?

Accepted Answer

$$\frac{1}{3}$$

Question 5

In a survey, 40 out of 100 people prefer tea over coffee. What is the empirical probability that a randomly selected person prefers tea?

Accepted Answer

$$0.4$$

Question 6

Which pair of events is mutually exclusive?

Accepted Answer

Drawing a red card and drawing a black card from a deck in a single draw

Question 7

If $$P(A) = 0.5$$ and $$P(B) = 0.3$$, and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$0.8$$

Question 8

A coin is tossed twice. What is the probability of getting at least one head?

Accepted Answer

$$0.75$$

Question 9

Which of the following is a discrete random variable?

Accepted Answer

The number of cars passing through a toll booth in an hour

Question 10

Given the probability distribution: $$P(X=0)=0.2$$, $$P(X=1)=0.5$$, $$P(X=2)=0.3. $$What is the mean ($$\mu) of$$ $$X$$?

Accepted Answer

$$1.1$$

Question 11

Which of the following tables represents a valid probability distribution?

Accepted Answer

X: 1, 2, 3; P(X): 0.2, 0.5, 0.3

Question 12

A binomial experiment consists of 5 trials with probability of success $$p=0.4. $$What is the probability of getting exactly 2 successes?

Accepted Answer

$$0.3456$$

Question 13

Which of the following is NOT a condition for a binomial distribution?

Accepted Answer

Each trial has more than two possible outcomes

Question 14

For a binomial distribution with $$n=10$$ and $$p=0.2$$, what is the mean ($$\mu$$)?

Accepted Answer

$$2$$

Question 15

Which statement best describes the standard normal distribution?

Accepted Answer

It is a normal distribution with mean $$0$$ and standard deviation $$1$$

Question 16

If the area to the left of $$z=1.5 in $$the standard normal distribution is $$0.9332$$, what is the area to the right?

Accepted Answer

$$0.0668$$

Question 17

In a normal distribution with mean $$\mu=50$$ and standard deviation $$\sigma=10$$, what is the $$z-$$score for $$x=70$$?

Accepted Answer

$$2$$

Question 18

According to the Central Limit Theorem, what happens to the distribution of sample means as the sample size increases?

Accepted Answer

It approaches a normal distribution regardless of the population's shape

Question 19

A population has mean $$\mu=100$$ and standard deviation $$\sigma=20. If a $$random sample of size $$n=25 is $$taken, what is the standard deviation of the sample mean ($$\sigma_{\bar{x}}$$)?

Accepted Answer

$$4$$

Question 20

A hospital records the time (in minutes) patients wait before seeing a doctor. Which variable is continuous?

Accepted Answer

The time each patient waits

Probability, Discrete Probability Distributions, and Normal Distributions: Study Guide

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