what is the probability that 100 lights in a 100 light set w

what is the probability that 100 lights in a 100 light set will remain lit for 2 years if each light has a 0.995 probability that it will remain lit for 2 years?

I think I would use the multiplication formula P(1 success) x P(1success)...= (0.995)100power

Solution

This is a problem for Binomial Distribution.

Here the trial is whether each light survives 2 year period. Obviously, the answer for this is either \"Yes\" or \"No\" i.e only two answer, making this a Bernoulli trial.

Let X be the random variable denoting the number of lights remaining lit for 2 years.

given, probability of success in a single trial= probability that it will remain lit for 2 years= .995

Required probability is given by

P(X=100)

= (100 C 100)*.995^100*(1-.995)^(100-100)    [where 100 C 100 denotes combination and is equal to 1]

= 1*.995^100*1

= .6057

[To the student:- You have though of the correct formula, but the real logic is given in the solution above]