Unit 4: Probability, Random Variables and Distributions

If [math] and [math], and [math] and [math] are independent, then [math]

The expected value of a discrete random variable is:

A binomial distribution requires all of the following conditions EXCEPT:

If [math], what is the mean of [math]?

The addition rule for probability states that [math]

The geometric distribution models:

If [math] and [math] are independent random variables with [math] and [math], then [math]

Conditional probability [math] is calculated as:

A continuous random variable differs from a discrete random variable in that:

Two events A and B are mutually exclusive. If P(A) = 0.3 and P(B) = 0.5, what is P(A or B)?

In a class, 60% of students pass the midterm, 80% pass the final, and 50% pass both. What is the probability a student passes the final given they passed the midterm?

Events A and B are independent. P(A) = 0.4 and P(B) = 0.3. What is P(A and B)?

P(A) = 0.6, P(B) = 0.5, and P(A and B) = 0.2. What is P(A or B)?

A bag contains 3 red and 5 blue marbles. Two marbles are drawn without replacement. What is the probability both are red?

A disease affects 1% of a population. A test for the disease is 95% accurate (both sensitivity and specificity). If a person tests positive, what is the approximate probability they actually have the disease?

A die is rolled 3 times. What is the probability of getting at least one six?

A bag has 4 red and 6 blue marbles. A marble is drawn, replaced, and another is drawn. What is P(both red)?

The law of large numbers states that:

What is the probability that a randomly selected student plays both sports and music?

Given that a student passed, what is the probability that they studied?