The probability that a music CD will last at least one year without failing is 0

Question

The probability that a music CD will last at least one year without failing is 0.95, calculate the probability that in a sample of 15;
a) 12 will last less than a year b) at most 5 will last less than a year c ) At least 2 lasting less than one year The probability that a music CD will last at least one year without failing is 0.95, calculate the probability that in a sample of 15;
a) 12 will last less than a year b) at most 5 will last less than a year c ) At least 2 lasting less than one year
a) 12 will last less than a year b) at most 5 will last less than a year c ) At least 2 lasting less than one year a) 12 will last less than a year b) at most 5 will last less than a year c ) At least 2 lasting less than one year

Explanation / Answer

P( music CD will last 1 year w/0 failing ) = .95

Therefore, P(music CD will last less than 1 year) = 1-.95 = .05

n = 15

So, n and p params of binomial distrbition are given and we can use them to solve the problem:

a. ) 12 will last less than a year = ?

P(X=12) = 15C12(.05^12)(.95^3) ~=0 ( it is .524 *10^-14 exactly)

b) P(X<=5) = P(X=0,1,2,3,4,5) = 0.99994

c) P(X>=2) = 1-P(X=0,1) = 0.17095

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