Q: If $$A$$ and $$B$$ are independent events, which equation correctly represents $$P(A \cap B)$$?

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

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

$$\frac{5}{10} \times \frac{4}{9}$$

Question 1

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

Accepted Answer

$$\frac{4}{6}$$

Question 2

Which of the following best describes the expected value of a random variable $$X$$?

Accepted Answer

The long-run average value of $$X$$, calculated as $$E[X] = \sum x_i P(x_i).$$

Question 3

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

Accepted Answer

$$\frac{19}{52}$$

Question 4

If $$A$$ and $$B$$ are independent events, which equation correctly represents $$P(A \cap B)$$?

Accepted Answer

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

Question 5

A Venn diagram is used to represent two events, $$A$$ and $$B. $$Which region represents $$A or$$ $$B$$?

Accepted Answer

The union of $$A$$ and $$B$$, denoted $$A \cup B.$$

Question 6

A medical test for a disease has a 95% sensitivity and 90% specificity. If 2% of the population has the disease, what is the probability that a randomly selected person tests positive?

Accepted Answer

$$0.029 (2.9$$%)

Question 7

Which formula correctly calculates the standard deviation of a sample of $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\sqrt{\frac{\sum_{i=1}^n (x_i - \bar{x})^2$}{n-1}}$$

Question 8

In a binomial experiment with $$n=10$$ trials and probability of success $$p=0.3$$, what is the probability of exactly 4 successes?

Accepted Answer

$$\binom{10}{4} (0.3)^4$ (0.7)^6$

Question 9

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

Accepted Answer

It has a skewness greater than zero.

Question 10

A student scores 85 on a test where the mean is 75 and the standard deviation is 5. What is the student's $$z-$$score?

Accepted Answer

$$z = \frac{85 - 75}{5} = 2$$

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

$$0.7$$

Question 12

Which of the following best describes conditional probability?

Accepted Answer

The probability of an event occurring given that another event has occurred.

Question 13

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

Accepted Answer

$$\frac{5}{10} 	imes \frac{4}{9}$$

Question 14

Which formula gives the probability of event $$A$$ given event $$B$$ has occurred?

Accepted Answer

$$P(A|B) = \frac{P(A \cap B)}{P(B)}$$

Question 15

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

Accepted Answer

$$\binom{3}{2} (0.5)^2$ (0.5)^1$

Question 16

Which of the following statements about sample space is correct?

Accepted Answer

It is the set of all possible outcomes of an experiment.

Question 17

If the probability of rain tomorrow is 0.3, what is the probability that it does NOT rain?

Accepted Answer

$$0.7$$

Question 18

Which of the following is a real-life example of a binomial distribution?

Accepted Answer

Counting the number of heads in 10 coin tosses.

Question 19

A student randomly guesses on a multiple-choice question with 4 options. What is the probability of guessing correctly?

Accepted Answer

$$\frac{1}{4}$$

Probability, Distributions, and Statistical Calculations: Review Notes

Study Guide - Practice Questions

Study Guide - Flashcards