Mutually Exclusive Events disjoint Events A and B

Mutually Exclusive Events (disjoint) Events A and B are mutually exclusive when only one can happen. A Ace B nine 1

Events are Not Mutually Exclusive Two events can occur at the same time. Red Ace Both red an ace 2

Multiplication Rule for INDEPENDENT Events Multiplication Rule for DEPENDENT Events Probability that both A and B occur Probability of A happening overall Probability of B happening given that A has happened

1. What is the probability of picking and queen from a deck of cards (if you replace the card after you pick)? 2. If you are rolling three dice, what is the probability that all three show a number less than 5? 3. Of the 13 pitchers on the Orioles, 5 are left-handers and 8 right-handers. If 2 pitchers are selected at random, what is the probability that at least one of them is righthander? P(at least one is right handed) = 1 – P(none are right) P(at least one is right handed) = 1 – (5/13)(4/12) P(at least one is right handed) = 1 – 0. 13 = 0. 87=87% 4

Example We have a standard deck of 52 cards. the probability of pulling out 1 What’s continued two aces in a row? p P(A 1 AND A 2) = P(A 1)P(A 2|A 1) P(A 1) = 4/52 p There are now 3 aces left in a 51 -card pack P(A 2|A 1) = 3/51 p Overall: P(A 1 AND A 2) = (4/52) (3/51) =. 0045 5

Compliments: the probability the event does not occur written as: P(Ac) or P(A’) Compliment Rule: P(A) = 1– P(Ac) Example: What is the probability of not rolling doubles? P(not rolling doubles) = 1 – P(doubles) = 1 – 6/36 = 30/36 = 83% 6