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}](https://tex.z-dn.net/?f=P%28X%3Dk%29%3D%5Cfrac%7Bn%21%7D%7Bk%21%28n-k%29%21%7D%5Ctimes%20p%5Ek%5Ctimes%20%281-p%29%5E%7Bn-k%7D)
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}](https://tex.z-dn.net/?f=P%28X%3D6%29%3D%5Cfrac%7B12%21%7D%7B6%21%2812-6%29%21%7D%5Ctimes%200.5%5E6%5Ctimes%20%281-0.5%29%5E%7B12-6%7D)
![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](https://tex.z-dn.net/?f=P%28X%3D6%29%3D%5Cfrac%7B12%5Ctimes%2011%5Ctimes%2010%5Ctimes%209%5Ctimes%208%5Ctimes%207%5Ctimes%206%21%7D%7B6%5Ctimes%205%5Ctimes%204%5Ctimes%203%5Ctimes%202%5Ctimes%206%21%7D%5Ctimes%200.015625%5Ctimes%200.015625)
![P(X=6)=11\times 2\times 3\times 2\times 7\times 0.015625\times 0.015625](https://tex.z-dn.net/?f=P%28X%3D6%29%3D11%5Ctimes%202%5Ctimes%203%5Ctimes%202%5Ctimes%207%5Ctimes%200.015625%5Ctimes%200.015625)
![P(X=6)=0.225](https://tex.z-dn.net/?f=P%28X%3D6%29%3D0.225)
Therefore, The probability that they each win six games is 0.225.
I think the answer to this question is 18
Here is what you might get. Hope it helps! Brainliest would be appreciated
Perimeter = side 1 + side 2 ´+ side 3.
Triangle 1
Perimeter = 6 + 8 + 10
= 24
Triangle 2
Perimeter = 9 + 12 + 15
= 36
Ratio
24/36 = 2/3
The ratio of the perimeters is also 2/3