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Chapter 4: Q.4.72 (page 168)

Two athletic teams play a series of games; the first team to win 4 games is declared the overall winner. Suppose that one of the teams is stronger than the other and wins each game with probability .6, independently of the outcomes of the other games. Find the probability, for i = 4, 5, 6, 7, that the stronger team wins the series in exactly i games. Compare the probability that the stronger team wins with the probability that it would win a 2-outof-3 series.

Short Answer

Expert verified

The probability that the stronger team will win in 2out of 3series is :210.62路0.4=0.288

Step by step solution

01

:Given Information

If i=4, the stronger team will win the series in exactly igames if and only if they win all four games. Hence, the Probability is 0.64=0.1296.

Suppose i鈭�{5,6,7}. Say that the lastithgame has won by the stronger team. Chose i-4places out of first i-1places and say that in these games has won weaker team. So, the probability that the stronger team has won the series in exactly igames isi-1i-40.64路0.4i-4.

02

Step 2:Explanation

i=5=0.207

i=6=0.207

i=7=0.1666

therefore the probability that the stronger team wins in 2out of 3series is ,210.62路0.4=0.288.

03

Final Answer

The final answer is210.62路0.4=0.288

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