Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

Exercises from Illustrative Mathematics A set of 5 exercises, commentary, and solutions

Students use the complement rule to calculate the probability of the complement of an event and the multiplication rule for independent events to calculate the probability of the intersection of two independent events.

Students recognize that two event A and B are independent if and only if P(A and B) = P(A)P(B) and interpret independence of two events A and B as meaning that the conditional probability of A given B is equal to P(A).

Students use the formula for conditional probability to calculate conditional probabilities and interpret probabilities in context.

Teacher and Student versions of full lesson from engageNY

Independent, Conditional, and Mutually Exclusive Events

Freezy's Ice Cream Stand doesn't think it has enough information to decide if it should add Pumpernickel Brickel or Dandy Cotton Candy to its menu. Therefore, it conducts another poll of its customers. It finds that the probability that a customer will like both flavors is 0.33 and the probability that a customer will like the Cotton Candy flavor is 0.8. What is the probability a customer will like the Pumpernickel flavor?

Lesson, videos, exercises, and text from CK-12. Additional resources available at this site.