This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MA/STAT416: Probability Lecture Notes Spring 2011 1 Chapter 3 January 26, 2011 3 Conditional Probability and Independence 3.1 Basic Formulas Basic Examples Example 1 . Find the conditional probability that the sum of two rolls of a fair die is 12, if the first roll is known to be six. Example 2 . Draw a card from a deck of 52 cards, what is the probability of getting a heart? Suppose now we already know that the card is not a club, what is the probability of getting a heart? If we dont know any other information, the probability is 13 52 . Now, given that the card is not a club, the probability becomes 1 3 . Conditional probability is used to model the probability of events when certain in formation is provided. Definition 3. For any two events A and B with P ( B ) > 0, the conditional proba bility of A given B has occurred denoted P ( A  B ), is defined by P ( A  B ) = P ( A B ) P ( B ) . General Multiplication Rule Rearranging the terms, we get the product rule for P ( A B ) : P ( A B ) = P ( A  B ) P ( B ) = P ( B  A ) P ( A ) . Example 4 . Let A , B be two events with P ( A ) = 0 . 5 and P ( B  A ) = 0 . 8. What is the probability that A and B will both happen? Example 5 . Let A be the event of getting a heart, B be the event of getting a 4. What is the conditional probability of A given B ? P ( A  B ) = P ( A B ) P ( B ) = 1 / 52 4 / 52 = 1 4 . Example 6 . Deal 2 cards from a deck of 52 cards (well shuffled, without replacement)....
View Full
Document
 Spring '08
 Staff
 Conditional Probability, Probability

Click to edit the document details