Question

There are four washing machines in an apartment complex: A, B, C, D. On any given day the probability that these machines break down is as follows: P(A) = 0.04, P(B) = 0.01, P(C) = 0.06, P(D) = 0.01 . Assume that the functionality of each machine is independent of that of others. What is the probability that on a given day at least one machine will be working?

Answer 1

Sal. Let, Event E= At least one machine will be wolking. It is given thad, PLA) = 0.04; P(B) = 0·0) : P(0) = 0.06 ; P(0) = 0-01 P(E) = 1-PCE) :P()*P(E) = 1} P(E) = All machine will not be wosiking P() = 1- P(È $ = functionality of each machine is >> PLE) = 1-(PLA). PLB). PCO).P(M) l independent of that of other si?

P(E) = 1-[P(A)=P(B).P(0). P(0)] P(E) = 1-((0.04) 0.01x0.06x0.01) PCE) = 1-0.00000024 1. P (E) = 0.99999976/the