The functioning of a particular machine is dependent on two safety valves: A and B. In order for the machine to operate perfectly BOTH valves must function well. Valve A has a 10% chance of failure while valve B has a 5% chance of failure. If you are in charge of maintaining this machine, then you can say that there is at worst a _____ chance of this machine breaking down and so with _____ chance the machine will work fine.
A) 10%; 90%
B) 15.5%; 84.5%
C) 1%; 99%.
D) 90%; 10%.

Question

Quizplus · Accepted Answer

The machine breaks down if either A or B fails. The probability of A working is 90% and B working is 95%. The probability of both working is 0.9 * 0.95 = 0.855 or 85.5%, meaning there's a 14.5% chance of failure. However, the question asks for the worst-case scenario, which involves adding the individual failure probabilities directly, leading to a misunderstanding in the calculation. The correct approach to find the breakdown chance is to calculate the failure probabilities directly or indirectly but considering the independence and combined probabilities correctly. The correct calculation for the machine to work fine is indeed the multiplication of both working probabilities, but the explanation provided initially was incorrect in suggesting a direct addition for the worst-case scenario. The correct worst-case scenario calculation should consider the probabilities of failure and success in a manner that accurately reflects the independence of the two events and their combined impact on the system's operation, which was not correctly described in the initial explanation.

The Functioning of a Particular Machine Is Dependent on Two