A string of lights contains 3 lights The lights are wired in

A string of lights contains 3 lights. The lights are wired in series, so that if any light fails the whole string will go dark. Each light has probability.10 of failing during a 2-year period. If the lights fail independently of each other, what is the probability that a string of lights will remain bright for 2 years?

Solution

The probability of whole string not failing , is each of the bulb not failing ,

so ,

P ( not failing ) = ( 1-0.1) *( 1-0.1) *( 1-0.1)

P ( not failing ) = 0.729