(10 points) Two players play a game that is a sequence of win/lose matches. The game...

    

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(10 points) Two players play a game that is a sequence of win/lose matches. The game continues until one player has won a total of 5 matches. Player A wins each individual match with probability 0.7. (a) What is the probability that player A will win the game? Answer this analytically and make sure to be clear about how you model this. (b) Write Mathematica code to simulate the game. Begin by generating a random variable X that is 1 with probability 0.7 and is 0 otherwise. Create a procedure that evaluates this RV until one player wins. Create another RV that is 1 when player A wins and is 0 otherwise. Use this to find the desired probability. (10 points) Two players play a game that is a sequence of win/lose matches. The game continues until one player has won a total of 5 matches. Player A wins each individual match with probability 0.7. (a) What is the probability that player A will win the game? Answer this analytically and make sure to be clear about how you model this. (b) Write Mathematica code to simulate the game. Begin by generating a random variable X that is 1 with probability 0.7 and is 0 otherwise. Create a procedure that evaluates this RV until one player wins. Create another RV that is 1 when player A wins and is 0 otherwise. Use this to find the desired probability.