What is the probability that the string of lights will remain bright?

Question

A string of 20 holiday lights is wired in series so that if any light fails, the whole string will go dark. Each light has a probability of 0.02 of failing during the holiday season. The lights fail independently of each other.

Answer 1

Darla,

         This a binomial trial. The success probability is 1-.02=.98, the bulbs are independent and there is only one way the string can stay lit so the probability is (.98)²⁰=.668

 

Hope this helps

 

Jim

Answer 2

You need to calculate the probability of at least one light failing. Since when one light fails the string goes dark.

 

P(at least one) = 1 - P(none fail) = 1 - (.98)²⁰.

 

Any questions? comment back...