Conditional Probability and the Multiplication Rule NOTES Coach Bridges.

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Conditional Probability and the Multiplication Rule

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Conditional Probability and the Multiplication Rule NOTES Coach Bridges

Conditional Probability Probability of an event occurring, given that another event has already occurred The conditional probability of event B occurring, given that event A has occurred, is denoted by P(B A) It is read as “probability of B, given A”

Example 1.Two cards are selected in sequence from a standard deck. Find the probability that the second card is a queen, given that the first card is a king. (Assume the King was not replaced)

Independent and Dependent Events Two events are independent if the occurrence of one of the events does not affect the probability of the occurrence of the other event Events that are not independent are dependent

Multiplication Rule Used to find the probability of two events occurring in sequence The probability that two events A and B will occur in sequence: –P(A and B) = P (A) times P(B A) If event A and B are independent, then the rule can be simplified to P(A and B) = P(A) times P(B)

Example of Multiplication Rule 1.Two cards are selected, without replacing the first card, from a standard deck. Find the probability of selecting a king and then selecting a queen? 2.A coin is tossed and a die is rolled. Find the probability of getting a head then rolling a 6.