Question

a piece of equipment will function only when three components A,B and C are working. The probability of A failing during one year is 0.15, that of B is failing is 0.05 and that of C failing is 0.10. what is the probability that the equipment will fail before the end of the year?

Answer 1

$P(failing)=1-P(not failing)$

=1-P(A not failing and B not failing and C not failing)

$=1-P(\bar{A}\bar{B}\bar{C})$

$=1-(0.85\times0.95\times0.9)=0.27325$