TS EAMCET · Maths · Probability
Three companies C1, C2, C3 produce car tyres. A car manufacturing company buys \(40 \%\) of its requirement from C1, \(35 \%\) from C2 and \(25 \%\) from C3. The company knows that \(2 \%\) of the tyres supplied by C1, \(3 \%\) by C2 and \(4 \%\) by C3 are defective. If a tyre chosen at random from the consignment received is found defective then the probability that it was supplied by C 2 is
- A \(\frac{7}{19}\)
- B \(\frac{12}{19}\)
- C \(\frac{10}{57}\)
- D \(\frac{26}{57}\)
Answer & Solution
Correct Answer
(A) \(\frac{7}{19}\)
Step-by-step Solution
Detailed explanation
\( P(D) = P(D|C_1)P(C_1) + P(D|C_2)P(C_2) + P(D|C_3)P(C_3) \) \( P(D) = (0.02)(0.40) + (0.03)(0.35) + (0.04)(0.25) \) \( P(D) = 0.008 + 0.0105 + 0.01 = 0.0285 \) \( P(C_2|D) = \frac{P(D|C_2)P(C_2)}{P(D)} \) \( P(C_2|D) = \frac{(0.03)(0.35)}{0.0285} \)…
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