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AP EAMCET · Maths · Probability

An item is tested on a device for its defectiveness. The probability that such an item is defective is 0.3. The device gives accurate result in 8 out of 10 such tests. If the device reports that an item tested is not defective, then the probability that it is actually defective is

  1. A \(\frac{2}{15}\)
  2. B \(\frac{3}{29}\)
  3. C \(\frac{3}{31}\)
  4. D \(\frac{4}{51}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{3}{31}\)

Step-by-step Solution

Detailed explanation

\( P(D) = 0.3 \) \( P(D') = 0.7 \) \( P(RND|D) = 1 - 0.8 = 0.2 \) \( P(RND|D') = 0.8 \) \( P(RND) = P(RND|D)P(D) + P(RND|D')P(D') \) \( P(RND) = (0.2)(0.3) + (0.8)(0.7) = 0.06 + 0.56 = 0.62 \) \( P(D|RND) = \frac{P(RND|D)P(D)}{P(RND)} \)…