Conditional Probability and Intersection of Events Section 13.3

Objective 1. Find the probability of one event and a second event occurring. 2. Compute conditional probabilities.

Key Term: Conditional Probability – the probability of event B, assuming that event A has already occurred, We denote this probability by P(B/A). Independent Events – two events that their occurrence has no effect on the probability of the other. Dependent Events – two events that their occurrence has an effect on the probability of the other.

Key Concept: Special Rule for Computing P(F/E) by Counting If E and F are events in a sample space with equally likely outcomes then P(F/E) = n(E ∩ F) = number of outcomes common to E and F n(E) number of outcomes in E

Key Concept: General Rule for Computing P(F/E) If E and F are events in a sample space with equally likely outcomes then P(F/E) = P(E ∩ F) P(E)

Example 1: Compute P(F/E) TB pg. 754/5

Example 2: Compute P(F/E) TB pg. 754/7

Example 3: Find the probability TB pg. 754/11

Example 4: Compute P(E/F) and P(F/E) TB pg. 754/15

Example 5: Find P(F/E) TB pg. 755/17

Example 6: Find P(F/E) TB pg. 755/19

Example 7: TB pg. 755/33

Example 8: TB pg. 755/37

Example 9: TB pg. 755/43

Key Concept: And Probabilities with Independent Events If A and B are independent events, then P(A and B) = P(A) * P(B). And Probabilities with Dependent Events If A and B are dependent events, then P(A and B) = P(A) * P(B given that A has occurred).

Example 10: TB pg. 755/47

Example 11: TB pg. 756/51

Example 12: TB pg. 756/55

Section 13.3 Assignment Classwork: ▫ TB pg. 754/6 – 20 Even, and 34 – 56 Even ▫ Remember you must write problem and show ALL work to receive credit for this assignment. ▫ DUE Tuesday, 11/ 22/11