Discussion
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
Answer: B
The probability is about 0.334.
Use Bayes' theorem. The probability that a shock absorber is reliable is:
\[ \begin{aligned} P(R) &= 0.6(0.96)+0.4(0.72) \\ &= 0.576+0.288 = 0.864 \end{aligned} \]
\[ P(Y \mid R) = \frac{0.288}{0.864} = \frac{1}{3} = 0.333 \]
The listed 0.334 is the nearest option to 1/3. 0.288 is the joint probability P(Y and R), not the conditional one; 0.667 is P(X | R); 0.720 is P(R | Y), the reverse conditional.
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