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An automobile plant contracted to buy shock absorbers from two suppliers \mathrm{X\: and \: \: Y}. \mathrm{X} supplies \mathrm{}60 \% and \mathrm{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 \mathrm{Y} is
 

Option: 1

0.288


Option: 2

0.334


Option: 3

0.667


Option: 4

0.720


Answers (1)

best_answer

Let \mathrm{{R}= }{Reliable Shock Absorber }

Given, \mathrm{" \quad P(X)=0.6, P(Y)=0.4,}

and \mathrm{P(R \mid X) =0.96, P(R \mid Y)=0.72 ,}

Now, \mathrm{ \quad P(Y \mid R) =\frac{P(X) P(R \mid Y)}{P(X) P(R \mid X)+P(Y) P(R \mid Y)} }

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

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

\mathrm{ =0.334 }



 

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Gaurav

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