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 Advanced Statistics Advanced Probability and Statistics Math Forum

 October 5th, 2013, 11:10 AM #1 Newbie   Joined: Oct 2013 Posts: 1 Thanks: 0 Probability question-- need help A and B are college football teams that have gone into overtime. In the first round A will go first with the following possible outcomes: no score; 3 points; 6 points; 7 points; 8 points; a turnover where B wins (note in this case the game ends immediately). The probabilities of these happening are: .2, .3, .1, .3, .09, .01. B then follows with the following conditional outcomes: if A scored 0�B ties with probability .1; B wins with probability .88; A wins with probability .02. if A scored 3�B ties with probability .3; B wins with probability .6; A wins with probability .1. if A scored 6�B ties with probability .01; B wins with probability .4; A wins with probability .59. if A scored 7�B ties with probability .3; B wins with probability .1; A wins with probability .6. if A scored 8�B ties with probability .2; A wins with probability .8 If the teams are tied after the first round, they go to a second round and continue until a team wins. a) Find the probability that: A wins in the first round; B wins in the first round; they�re tied after the first round. b) Find the probability that A wins. c) Find the expected number of rounds. I figured out part a) 0.345, 0.436, and 0.219. Not sure how to do parts b and c. Help! thanks  October 7th, 2013, 04:08 PM #2 Senior Member   Joined: Jul 2012 From: DFW Area Posts: 642 Thanks: 99 Math Focus: Electrical Engineering Applications Re: Probability question-- need help Hi MathNoob123, and welcome to the forums. I agree with your calculations for part a). Let's use those probabilities to find b) and c): The probability of A winning is the probability of A winning in the first round (0.345) plus that of the second round, and so on. The probability of a tie (0.219) factors in as follows: The infinite sum inside the parenthesis is: so: The expected value is the sum of the round number times that round's probability of ending the game: The infinite sum inside the parenthesis is: so: One comment, although I am not an expert: The statement "if A scored 0�B ties with probability .1; B wins with probability .88; A wins with probability .02." seems incomplete. The only way that A can win in that round is if B turns the ball over, and that is not specifically stated. I assumed that this is the case. Tags probability, question Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post jskrzy Probability and Statistics 4 October 31st, 2011 02:11 PM skate_rds Advanced Statistics 3 March 17th, 2011 07:37 AM skate_rds Advanced Statistics 0 February 6th, 2011 09:16 PM madflame991 Probability and Statistics 0 February 1st, 2011 01:06 AM tnutty Advanced Statistics 1 January 27th, 2011 04:31 PM

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