advertisement

Mutually Exclusive Events Probability of Mutually Exclusive Events In some situations, more than one event could occur during a single trial. Mutually Exclusive events are said to be Disjoint. The 2 outcomes could not happen simultaneously Addition Rule for Mutually Exclusive Events When events A and B are mutually exclusive, the probability that A or B will occur is given by the addition rule for mutually exclusive events P( AorB) P( A) P( B) Ex Teri attends a fundraiser where 15 T-shirts are being given away at the door. The winners are randomly given a shirt from a stock of 2 black, 4 blue, 9 white shirts. Teri really likes the black and blue shirts. Assuming that Teri wins first, What is the probability that she will get the shirt that she likes. Let A represent the event Teri wins a black Shirt Let B represent the event Teri wins a blue shirt Teri would be happy if either A or B occurred 2 P ( A) 15 4 P( B) 15 P( AorB) P( A) P( B) 2 4 P( AorB) 15 15 6 15 2 5 Non- Mutually Exclusive Events The Events CAN occur simultaneously Ex: on a board game you need to roll either an 8 or a double You can roll and eight and a double with 4 and 4. P(8) 5 36 P(double) 1 6 P(8ordouble) 5 1 36 6 You need to take into consideration that you counted (4,4) twice Addition rule for Non-Mutually Exclusive Events When events A and B are nonmutually exclusive events, the probability that A or B will occur is given by the addition rule for nonmutually exclusive events P( AorB) P( A) P( B) P( AandB) Ex A card is randomly selected from a standard deck of 52 cards. What is the Probability that either a heart or a face card (jack, queen or king) is selected? Let A be the event that a heart is selected. Let B be the event that a face card is selected. 13 P ( A) 52 12 P( B) 52 But the King, Queen and Jack of Hearts are in Both A and B!!!!!! P( AorB) P( A) P( B) P( AandB) 13 12 3 P( AorB) 52 52 52 22 52 11 26 Ex An auto parts manufacturer is testing a product to see whether it requires a special coating to prevent rusting. -The quality control testing show that rust has a 0.2% probability of damaging the part. -It also has a 0.6% chance of damaging parts that are attached to it. -Lastly there is a 0.1% probability of damaging both the part and other parts it will be attached to. Determine the probability that rust will damage the products. P( AorB) P( A) P( B) P( AandB) P( AorB) 0.2% 0.6% 0.1% 0.7% Homework! Pg 340 #1,2,3, 4a, 5,7,11,13 HAND IN 11 and 13 for Assessment