Conditional Probability and Independence. Learning Targets 1. I can use the multiplication rule for independent events to compute probabilities. 2. I.

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Presentation transcript:

Conditional Probability and Independence

Learning Targets 1. I can use the multiplication rule for independent events to compute probabilities. 2. I can compute conditional probabilities.

Conditional Probability The probability that one event happens given that another event is already known to have happened is called a conditional probability. Suppose we know that event A has happened. Then the probability that event B happens given that event A has happened is denoted by P(B A).

Independent Events Two events A and B are independent if the occurrence of one event has no effect on the chance that the other event will happen. In other words events a and B are independent if P(A | B) = P(A) and P(B | A) = P(B).

Dependent Events Multiplication rule for independent events. If A and B are independent events, then the probability that A and B both occur is

General Multiplication Rule

Conditional Probability Formula To find the conditional probability P(B A), use the formula

First Trimester Screen The First Trimester Screen is a noninvasive test given during the first trimester of pregnancy to determine if there are specific chromosomal abnormalities in the fetus. According to a study published in the New England Journal of Medicine in November 2005, approximately 5% of normal pregnancies will receive a positive result. Among 100 women with normal pregnancies, what is the probability that there will be at least 1 false positive?

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