The probability that Ravi passes a driving test is 0.7 and the probability that Sita passes it is 0.6. Their results are independent of each other. The probability that Ravi passes and Sita does not pass is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.28
Let R be the event that Ravi passes and S the event that Sita passes. Sita does not pass with probability
\(P(S') = 1-0.6 = 0.4\)
Since R and S are independent, R and S’ are also independent, so the probabilities multiply:
\(P(R\cap S') = P(R)\times P(S') = 0.7\times 0.4 = 0.28\)
Why the other options are incorrect
Option (1) 0.42 — Incorrect. This is \(0.7\times 0.6\), the chance that both pass.
Option (3) 0.18 — Incorrect. This is \(0.3\times 0.6\), the chance that Sita passes and Ravi does not.
Option (4) 0.12 — Incorrect. This is \(0.3\times 0.4\), the chance that neither of them passes.