SOLUTION: Eight percent of all college graduates hired by companies stay with the same company for more than five years. The probability, rounded to four decimal places, that in a random sam

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Question 1194836: Eight percent of all college graduates hired by companies stay with the same company for more than five years. The probability, rounded to four decimal places, that in a random sample of 11 such college graduates hired recently by companies, exactly 4 will stay with the same company for more than five years is
Answer by math_tutor2020(3817) About Me  (Show Source):
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p = probability of success
p = probability of a person staying with the same company for more than five years
p = 0.08

n = sample size
n = 11

Binomial Probability Formula
P(x) = ( nCx ) * p^x * (1-p)^(n-x)
P(4) = ( 11C4 ) * 0.08^4 * (1-0.08)^(11-4)
P(4) = ( 330 ) * 0.08^4 * (1-0.08)^(11-4)
P(4) = 0.0075403009396 approximately
P(4) = 0.0075

The 11C4 refers to the nCr notation
The scratch work is shown below
n = 11, r = 4
n C r = (n!)/(r!(n-r)!)
11 C 4 = (11!)/(4!*(11-4)!)
11 C 4 = (11!)/(4!*7!)
11 C 4 = (11*10*9*8*7!)/(4!*7!)
11 C 4 = (11*10*9*8)/(4!)
11 C 4 = (11*10*9*8)/(4*3*2*1)
11 C 4 = (7920)/(24)
11 C 4 = 330

Answer: 0.0075 (approximate)