Question

A machine has four components, A, B, C, and D, set up in such a manner that all four

parts must work for the machine to work properly. Assume the probability of one part
working does not depend on the functionality of any of the other parts. Also assume
that the probabilities of the individual parts working are P(A)=P(B) =0.97, P(C) =
0.99, and P(D)=0.93. Find the probability that the machine works properly. Round
to the nearest ten-thousandth.
A) 0.8931
B) 0.1337
C) 0.9355
D) 0.8663
E) None of the answers

Answer 1

D)

Explanation:

so, it simply means that all 4 events (the 4 machine parts work) are one combined event.

so, the probability that the machine works properly is the product of the 4 single probabilities :

0.97 × 0.97 × 0.99 × 0.93 = 0.86628663 ≈ 0.8663