Multiple choice

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' 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

  1. 0.288

  2. 0.334

  3. 0.667

  4. 0.720

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using Bayes' Theorem: P(Y|Reliable) = P(Reliable|Y) * P(Y) / [P(Reliable|Y) * P(Y) + P(Reliable|X) * P(X)]. P(Y|Reliable) = (0.72 * 0.40) / (0.72 * 0.40 + 0.96 * 0.60) = 0.288 / (0.288 + 0.576) = 0.288 / 0.864 = 0.3333.