Statistics: Probability Rules

Which of the following events are independent?

• Drawing a King from a deck of cards and rolling a 5 on a die

• Having a high GPA and getting a college scholarship for academics

• The age of a driver and their likelihood of being in a car accident

• Having brown hair and brown eyes

Answer explanation

Independent means there is no relationship between the two events - they do not affect each other.

A survey shows that 50% of adults in America approve of the president's recent policy statements. You select three adults at random. What is the probability that they all approve of the statements?

Answer explanation

ALL means the first AND the second AND the third approve of the statements. AND means multiply.

Ms. Timlin collected data from her students and found that 45% have brown eyes, 20% have blue eyes, and the rest have other colored eyes. If you select a student at random, what is the probability that they have brown or blue eyes?

If A and B are independent, then you can ___ their probabilities to find the probability of A ___ B

• multiply, and

• add, and

• multiply, or

• add, or

If A and B are mutually exclusive, then you can ___ their probabilities to find the probability of A ___ B

• multiply, and

• add, and

• multiply, or

• add, or

What do you call a random variable with possible values that form a finite or countable set?

• continuous

• discrete

• finite

• infinite

What term is used to describe the average value of a discrete random variable over numerous trials of an experiment?

• mean

• probability

• standard deviation

• variance

Which of the following represents the mean value of a discrete random variable?

• Expected value

• Median

• Standard deviation

• Standard deviation

Which of the following is the correct formula to find the expected value of the probability distribution?

• E(x) = ∑[x ∙ P(x)]

• E(x) = ∑[x²∙ P(x)]

• E(x) = ∑[x² ∙ P(x)] − u²

Which of the following rules state that almost all data fall within the 1, 2, and 3 Standard Deviation of the Mean when the population is normally distributed?

• Empirical rule

• Lottery rule

• Pascal’s triangle rule

• Sampling rule