Three companies C_1, C_2, C_3 produce car tyr | vedclass

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(A) Let $E_1, E_2, E_3$ be the events that the tyre is supplied by companies $C_1, C_2, C_3$ respectively. Let $D$ be the event that the chosen tyre i

Vedclass · Accepted Answer

$\frac{7}{19}$

Vedclass · Answer

(A) Let $E_1, E_2, E_3$ be the events that the tyre is supplied by companies $C_1, C_2, C_3$ respectively. Let $D$ be the event that the chosen tyre is defective.Given probabilities are:$P(E_1) = 0.40, P(E_2) = 0.35, P(E_3) = 0.25$$P(D|E_1) = 0.02, P(D|E_2) = 0.03, P(D|E_3) = 0.04$Using Bayes' Theorem,the probability that the defective tyre was supplied by $C_2$ is $P(E_2|D) = \frac{P(E_2)P(D|E_2)}{P(E_1)P(D|E_1) + P(E_2)P(D|E_2) + P(E_3)P(D|E_3)}$$P(E_2|D) = \frac{0.35 	imes 0.03}{(0.40 	imes 0.02) + (0.35 	imes 0.03) + (0.25 	imes 0.04)}$$P(E_2|D) = \frac{0.0105}{0.008 + 0.0105 + 0.0100} = \frac{0.0105}{0.0285}$$P(E_2|D) = \frac{105}{285} = \frac{21}{57} = \frac{7}{19}$

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