A plant has two machines Machine 1 is three times more likel

A plant has two machines. Machine 1 is three times more likely to malfunction than machine 2. The probability that both machines malfunction is 0.03. Assuming that malfunction of machine 1 is independent of that of machine 2, what is the probability that both machines function well?

Solution

Machine 1 is three times more likely to malfunction than machine 2. The probability that both machines malfunction is 0.03.

Thus, x*3x=0.03

x=0.1

Thus the probability that machine 1 works well is 1-0.1*3=0.7

The probability that machine 2 works well is 1-0.1=0.9

Thus the probability that both machines works well is: 0.7*0.9=0.63