Quiz 2 - Stat 225 Quiz 02 Spring 2012 Name You have 10...

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1 ( ) ( )* ( | ) n i i i P A P B P A B 1 ( )* ( | ) ( | ) ( )* ( | ) j j j n i i i P B P A B P B A P B P A B ( ) ( | ) ( ) P A B P A B P B ( ) 1 ( ) C P A P A   ( ) ( ) ( ) ( ) P A B P A P B P A B ( ) ( )* ( | ) P A B P B P A B Stat 225 - Quiz 02 Name ________________________________________ Spring 2012 You have 10 minutes to complete the problem below. Show sufficient work to receive full credit. You must work on the problem you are given: trading quiz sheets will result in a 0 for both parties. If a decimal answer is not exact, please round to 4 decimal places. 1. The Patriots are playing the Giants in the Super Bowl. The Patriots have a probability of .75 of winning the game. Keep in mind there are no ties in the post-season (Donovan McNabb). If the Patriots win, they will win be at least 10 points with a probability of .7. If the Giants win, they will win by at most 9 with a probability of .9. (a) Draw a tree diagram with the appropriate probabilities filled in. (5 points) (b) What is the probability that the game is decided by 10 or more points? (6 points) (c) If the game was won by 10 or more points, what is the probability that the Patriots won? (5 points) (d) Are the events the Patriots winning and winning by at least 10 points independent? Prove your answer. (4 points)
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1 ( ) ( )* ( | ) n i i i P A P B P A B 1
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