Q: If two events E and F are independent, which of the following is always true?

$$P(E \text{ and } F) = P(E) \cdot P(F)$$

Question 1

Which of the following pairs of events are independent?

Accepted Answer

Flipping a coin and rolling a die

Question 2

If $$P(E) = 0.4$$ and $$P(F) = 0.5$$, and E and F are independent, what is $$P(E 	ext{ and } F)$$?

Accepted Answer

$$0.2$$

Question 3

Suppose the probability that a randomly selected 24-year-old male will survive the year is $$0.9986. $$What is the probability that three randomly selected 24-year-old males will all survive the year?

Accepted Answer

$$(0.9986)^3$$

Question 4

If the probability that a 24-year-old male survives the year is $$0.9986$$, what is the probability that at least one out of 1000 randomly selected 24-year-old males will die during the year?

Accepted Answer

$$1 - (0.9986$$)^{1000}$$

Question 5

Which of the following statements is TRUE about disjoint and independent events?

Accepted Answer

If two events are disjoint and both have positive probability, they are not independent.

Question 6

Given the table, what is the probability that a randomly selected individual is female and divorced?

Accepted Answer

$$\frac{16.6}{271.7}$$

Question 7

Using the table, what is the probability that a randomly selected individual has never married, given that the individual is male?

Accepted Answer

$$\frac{49.5}{133.6}$$

Question 8

Suppose 0.22% of all births result in a preterm baby who weighs 8 pounds, 13 ounces or more, and 12.7% of all births are preterm. What is the probability that a randomly selected preterm baby weighs 8 pounds, 13 ounces or more?

Accepted Answer

$$\frac{0.0022}{0.127}$$

Question 9

If $$P(E) = 0.3$$ and $$P(F|E) = 0.5$$, what is $$P(E 	ext{ and } F)$$?

Accepted Answer

$$0.15$$

Question 10

A speeding driver has a 0.8 probability of being pulled over and a 0.9 probability of getting a ticket if pulled over. What is the probability that a randomly selected speeding driver gets pulled over and gets a ticket?

Accepted Answer

$$0.8 	imes 0.9$$

Question 11

If $$P(E) = 0.6$$, $$P(F) = 0.7$$, and E and F are independent, what is $$P(E 	ext{ or } F)$$?

Accepted Answer

$$0.88$$

Question 12

Given the table, what is the probability that a randomly selected individual is male, given that the individual is widowed?

Accepted Answer

$$\frac{3.5}{15.0}$$

Question 13

If two events E and F are independent, which of the following is always true?

Accepted Answer

$$P(E 	ext{ and } F) = P(E) \cdot P(F)$$

Question 14

A fair die is rolled. What is the probability that the outcome is 3, given that the outcome is odd?

Accepted Answer

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

Question 15

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

Accepted Answer

$$0.2$$

Question 16

Which of the following is the correct formula for the complement rule?

Accepted Answer

$$P(E^c) = 1 - P(E)$$

Question 17

Suppose you roll a fair die twice. What is the probability of rolling a 6 both times?

Accepted Answer

$$\frac{1}{36}$$

Question 18

If $$P(E) = 0.7$$ and $$P(F|E) = 0.2$$, what is $$P(E 	ext{ and } F)$$?

Accepted Answer

$$0.14$$

Question 19

Which of the following best describes the difference between independent and disjoint events?

Accepted Answer

Independent events do not affect each other's probabilities, while disjoint events cannot occur together.

Probability: Independence, Multiplication Rule, and Conditional Probability

Study Guide - Practice Questions

Study Guide - Flashcards