Topic: Engineering Mathematics
A person on a trip has a choice between private car and public transport. The probability of using a private car is 0.45. While using public transport, further choice available are bus and metro. Out of which the probability of commuting by a bus is 0.55. In such a situation, the probability (rounded upto two decimals) of using a car, bus and metro respectively would be
- A. 0.45, 0.30 and 0.25
- B. 0.45, 0.25 and 0.30
- C. 0.45, 0.55 and 0
- D. 0.45, 0.35 and 0.20
Answer: A. 0.45, 0.30 and 0.25
Explanation: Probability of using a private car = 0.45.
Probability of using public transport = $1 - 0.45 = 0.55$.
Probability of using a bus (given public transport) = $0.55 \times 0.55 = 0.3025 \approx 0.30$.
Probability of using a metro (given public transport) = $0.55 \times (1 - 0.55) = 0.55 \times 0.45 = 0.2475 \approx 0.25$.