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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