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A person goes to the office either by a car, or scooter, or bus, the probability of which being 2 7 , 3 7 , 2 7 respectively. The probability that he reaches office late if he takes a car, or scooter, or bus is 2 9 , 1 9 , 4 9 respectively. If he reaches office in time, the probability that he travelled by car is k , then the value of 24 k + 7 is equal to

Options

  1. A7
  2. B14
  3. C21 2
  4. D31 2

Correct answer

B. 14

Step-by-step solution

Let, C , B , S be the events such that a person goes to the office by car, bus or scooter respectively. P C = 2 7 , P S = 3 7 , P B = 2 7 Let, T be the event that he reaches office in time P T C = 7 9 , P T S = 8 9 , P T B = 5 9 P C T = P C P T C P C P T C + P B P T B + P S P T S = 2 7 × 7 9 2 7 × 7 9 + 3 7 × 8 9 + 2 7 × 5 9 = 14 48 = 7 24

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