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Nady [450]
3 years ago
14

A computer chess game and a human chess champion are evenly matched. They play twelve games. Find probabilities for the followin

g events. (Round all answers to four decimal places.) (a) They each win six games.
Mathematics
1 answer:
sleet_krkn [62]3 years ago
3 0

Answer:

The probability that they each win six games is 0.225.      

Step-by-step explanation:

Given : A computer chess game and a human chess champion are evenly matched. They play twelve games.

To find : The probability that they each win six games?

Solution :

Applying binomial distribution,

Here n=12 and p=0.5

P(X=k)=\frac{n!}{k!(n-k)!}\times p^k\times (1-p)^{n-k}

The probability that they each win six games is k=6.

P(X=6)=\frac{12!}{6!(12-6)!}\times 0.5^6\times (1-0.5)^{12-6}

P(X=6)=\frac{12\times 11\times 10\times 9\times 8\times 7\times 6!}{6\times 5\times 4\times 3\times 2\times 6!}\times 0.015625\times 0.015625

P(X=6)=11\times 2\times 3\times 2\times 7\times 0.015625\times 0.015625

P(X=6)=0.225

Therefore, The probability that they each win six games is 0.225.

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