Question taken from the book Intro to Probability Theory Cha

Question taken from the book: Intro to Probability Theory Chap 1 by Hoel, Port, Stone

A machine consists of 4 components linked in parallel, so that the machine fails only if all four components fail. Assume component failures are independent of each other. If the components have probabilities .1, .2, .3, and .4 of failing when the machine is turned on, what is the probability that the machine will function when turned on

Solution

Note that

P(at least one work) = 1 - P(none works) = 1 - P(all fail)

Hence,

P(at least one work) = 1 - 0.1*0.2*0.3*0.4 = 0.9976 [ANSWER]