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KVPY2018MathematicsProbability

The probability of men getting a certain disease is 1 2 and that of women getting the same disease is 1 5 . The blood test that identifies the disease gives the correct result with probability 4 5 . Suppose a person is chosen at random from a group of 30 males and 20 females, and the blood test of that person is found to be positive. What is the probability that the chosen person is a man?

Options

  1. A75 107
  2. B3 5
  3. C15 19
  4. D3 10

Correct answer

A. 75 107

Step-by-step solution

We have 30 males and 20 females. P males = 30 50 = 3 5 P females = 20 50 = 2 5 Required probability = 1 + 3 1 + 3 + 5 + 7 = 3 5 × 1 2 × 4 5 + 3 5 × 1 2 × 1 5 3 5 × 1 3 × 4 5 + 3 5 × 1 2 × 1 5 + 2 5 × 1 5 × 4 5 + 2 5 × 4 5 × 1 5 = 15 50 15 50 + 16 125 = 75 107

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