Question

NEED LAST 2

Two individuals, A and B, are finalists for a chess championship. They will play a sequence of games, each of which can result in a win for A, a win for B, or a draw. Suppose that the outcomes of successive games are independent, with P(A wins game) = 0.3, P(B wins game) = 0.2, and P(draw) = 0.5. Each time a player wins a game, he earns 1 point and his opponent earns no points. The first player to win 5 points wins the championship. (a) What is the probability that A wins the championship in just five games? (Enter your answer to five decimal places.) .0024300 (b) What is the probability that it takes just five games to obtain a champion? (Enter your answer to five decimal places.) 00032000 X (c) If a draw earns a half-point for each player, describe how you would perform a simulation to estimate P(A wins the championship). Assume that the championship will end in a draw if both players obtain 5 points at the same time. Use a random number table, and let the numbers 0-2 represent A winning the game and the numbers 3-4 represent B winning, then 5-9 represents the game resulting in a draw. Simulate games until one competitor wins or there is a draw, and repeat a large number of times. Then the probability of A winning the championship is estimated by (number of runs where A wins)/(total number of runs). Use a random number table, and let the numbers 0-2 represent A winning the game and the numbers 3-4 represent B winning, then 5-9 represents the game resulting in a draw. Simulate games until one competitor wins or there is a draw, and repeat a large number of times. Then the probability of A winning the championship is estimated by (number of runs where B wins)/(total number of runs). Use a random number table, and let the numbers 0-1 represent A winning the game and the numbers 2-6 represent B winning, then 7-9 represents the game resulting in a draw. Simulate games until one competitor wins or there is a draw, and repeat a large number of times. Then the probability of A winning the championship is estimated by (number of runs where A wins)/(total number of runs). Use a random number table, and let the numbers 0-2 represent B winning the game and the numbers 3-4 represent A winning, then 5-9 represents the game resulting in a draw. Simulate games until one competitor wins or there is a draw, and repeat a large number of times. Then the probability of A winning the championship is estimated by (number of runs where A wins)/(total number of runs). Use a random number table, and let the numbers 0-4 represent A winning the game and the numbers 5-7 represent B winning, then 8-9 represents the game resulting in a draw. Simulate games until one competitor wins or there is a draw, and repeat a large number of times. Then the probability of A winning the championship is estimated by (number of runs where A wins)/(total number of runs).

Answer 1

a)P(A wins ) =P(wins first 5 games) =0.3^5=0.00243

b)P(ends in 6 games) =P(A wins first 5 games)+P(B wins first 5 games)=0.3^5+0.2^5 =0.00275

c)

Use a random number table, and let the numbers 0-2 represent A winning the game and the numbers 3-4 represent 8 winning, then 5-9 represents the game resulting in a draw. Simulate games until one competitor wins or there is a draw, and repeat a large number of times. Then the probability of A winning the championship is estimated by (number of runs where A wins)/(total number of runs).