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Conditional Probability

# Conditional Probability - Conditional Probability Un...

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Conditional Probability Un Problem: A math teacher gave her class two tests. 25% of the class passed both tests and 42% of the class passed the first test. What percent of those who passed the first test also passed the second test? Analysis: This problem describes a conditional probability since it asks us to find the probability that the second test was passed given that the first test was passed. In the last lesson, the notation for conditional probability was used in the statement of Multiplication Rule 2. Multiplication Rule 2: When two events, A and B, are dependent, the probability of both occurring is: The formula for the Conditional Probability of an event can be derived from Multiplication Rule 2 as follows: Start with Multiplication Rule 2. Divide both sides of equation by P(A). Cancel P(A)s on right-hand side of equation. Commute the equation.

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We have derived the formula for conditional probability. Now we can use this formula to solve the problem at the top of the page. Problem: A math teacher gave her class two tests. 25% of the class passed both tests and 42% of the class passed the first test. What percent of those who passed the first test also passed the second test?
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Conditional Probability - Conditional Probability Un...

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