An electrical appliance will not work unless component QK does. Component QK's reliability is 0.95. Every other part of the appliance is 100 percent reliable. What would the reliability of the appliance be if a backup QK were added?
A) .95
B) .9975
C) .9025
D) .9205
E) .9795

Question

Quizplus · Accepted Answer

The reliability of the appliance with only one QK component working is 0.95. This means that the probability of the appliance working is 0.95 or 95%.

Now, if a backup QK component is added, the appliance will work if at least one of the QK components works. This is known as a "parallel" system, where the system works if any individual component works.

The reliability of a parallel system with two components can be calculated using the formula:

R(total) = (R(A) + R(B) - R(A) x R(B)),

where R(A) and R(B) are the reliabilities of the two components.

In this case, both components are identical, so we can simplify the formula to:

R(total) = 2R - R^2,

where R is the reliability of each individual component (0.95).

Plugging in the values, we get:

R(total) = 2 x 0.95 - 0.95^2 = 0.9975

Therefore, the reliability of the appliance with a backup QK component is 0.9975 or 99.75%.

The correct answer is B.

An Electrical Appliance Will Not Work Unless Component QK Does