Chapter 5 (Cumulative) Review

What’s the formula to calculate the probability of an event occurring?

P(X) = # of possibilities that meet the condition / total # of possibilities

What are Mutually Exclusive Events?

When 2 events, A and B, cannot happen at the same time.

What does the Law of Large #’s say?

The experimental probability of an event gets closer to the theoretical (actual) probability of that event happening with more and more experiments.

How do you calculate AND probabilities P(A AND B)?

You only count events where A and B happen at the SAME TIME.

How do you calculate OR probabilities P(A OR B)?

P(A OR B) = P(A) + P(B) - P(A AND B)

What is P(A AND B) equal to for Mutually Exclusive Events?

P(A AND B) = 0

How do you interpret conditional probabilities? (use P(A | B) to describe this!)

P(A | B) = Probability of event A and B both happening / Probability of event B happening.

What formula do you use to check for independence?

P(A) = P(A | B)

What is the formula for Bayes Theorem?

P(A | B) = [P(B | A) * P(A)] / P(B)

When should you use Decision Trees?

When the problem mentions multiple probabilities in order and you’re given a piece of information and asked to solve for a probability.

When do you use the proportion method in Decision Trees?

When you’re given information about a person/object of interest and asked to calculate a probability.

When do you use the chain multiplication method in Decision Trees?

When you’re asked to find the probability of something happening, and you’re not given any information about a person/object.

What is the formula for Independent Events?

P(A AND B) = P(A) * P(B) or, just multiply probabilities directly.

What is the General Multiplication Rule?

P(A and B) = P(A) * P(B | A)

What are the 2 formulas used for interpreting “at least one” events?

• P(at least 1 failure) = 1 - P(all successes for people in the sample)

• P(at least 1 success) = 1 - P(all failures for people in the sample)

What tool should you use when you don’t know a probability and the question involves 2 variables?

Use a Two-Way table.