SOLUTION: Find the probability of this trial, x = 8, n = 11, p = 0.9, where x is successes in n trials. a. 9% b. 7% c. 19%

Question 1087907: Find the probability of this trial, x = 8, n = 11, p = 0.9, where x is successes in n trials.
a. 9%
b. 7%
c. 19%
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
We have n = 11 as the sample size, p = 0.9 as the probability of success, and k = 8 as the number of successes (I'm using k instead of x)

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Plug in n = 11 and k = 8 into the combination formula below

n C k = (n!)/(k!*(n-k)!)

11 C 8 = (11!)/(8!*(11-8)!)

11 C 8 = (11!)/(8!*3!)

11 C 8 = (11*10*9*8!)/(8!*3!)

11 C 8 = (11*10*9)/(3!)

11 C 8 = (11*10*9)/(3*2*1)

11 C 8 = 990/6

11 C 8 = 165

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Using that combination value, we can say

P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k)

P(X = 8) = (11 C 8)*(0.9)^(8)*(1-0.9)^(11-8)

P(X = 8) = (11 C 8)*(0.9)^(8)*(0.1)^(3)

P(X = 8) = (165)*(0.9)^(8)*(0.1)^3

P(X = 8) = (165)*(0.43046721)*(0.001)

P(X = 8) = 0.07102708965

P(X = 8) = 0.07

P(X = 8) = 7% (move the decimal 2 spots to the right to go from 0.07 to 7%)

This means that the answer is Choice B
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