Introducing Conditional Probability (4.2.1)

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Presentation transcript:

Introducing Conditional Probability (4.2.1) March 3rd, 2017

number of outcomes in (A and B) Vocabulary & Notation *Conditional Probability: The probability that event B occurs, given that event A has already occurred, written as “the probability of B given A” number of outcomes in (A and B) number of outcomes in A *Look for key parts of phrases, like “find the probability of ____ given _____” or what is the probability of ______if _______”.

Ex. 1: Nate rolls a pair of 6-sided dice (also called number cubes) Ex. 1: Nate rolls a pair of 6-sided dice (also called number cubes). What is the probability that both numbers are prime if their sum 7?

Independent Events & Conditional Probability *Recall that for Independent Events, we know Therefore,

Ex. 2: Masanori rolls a number cube 3 times Ex. 2: Masanori rolls a number cube 3 times. Consider the following events. A: The first roll is an even number. B: There are at least two even numbers. Determine if A and B are independent events.

Ex. 3: Last year in Mrs. MT’s Calculus class 92% of students received a passing score on the Advanced Placement exam. That same year, 25% of those students also received an A in the Calculus class. What is the probability that a student who passed the AP Exam also got an A in the class?