Question

An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of X's shock absorbers, 96% are reliable. Of Y's shock absorbers, 72% are reliable.

The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is

• A. 0.288
• B. 0.334
• C. 0.667
• D. 0.720

Answer 1

The correct option is B 0.334

Let R = {Reliable Shock Absorber}

Given, P(X) = 0.6, P(Y) = 0.4,

and P(R|X) = 0.96, P(R|Y) = 0.72
By Baye's theorem
$P\left(Y|R\right)=\frac{P\left(Y\right)P\left(R|Y\right)}{P\left(X\right)P\left(R|X\right)+P\left(Y\right)P\left(R|Y\right)}$

$=\frac{0.4\times 0.72}{0.6\times 0.96+0.4\times 0.72}$

$=\frac{0.288}{0.576+0.288}=\frac{0.288}{0.864}$

= 0.334