The probability that a student passes in Mathematics is 0.8. If the student passes in Mathematics, the probability that the student also passes in Physics is 0.6. The probability that the student passes in both Mathematics and Physics is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0.48
Let M be the event that the student passes in Mathematics and P the event that the student passes in Physics. The second figure is a conditional probability:
\(P(M) = 0.8,\quad P(P|M) = 0.6\)
By the multiplication theorem:
\(P(M\cap P) = P(M)\,P(P|M)\)
\(P(M\cap P) = 0.8\times 0.6 = 0.48\)
Why the other options are incorrect
Option (1) 0.75 — Incorrect. This is \(\frac{0.6}{0.8}\); the two probabilities must be multiplied, not divided.
Option (2) 0.32 — Incorrect. This is \(0.8\times 0.4\), the probability of passing in Mathematics but failing in Physics.
Option (3) 0.60 — Incorrect. This is P(P|M) itself; it still has to be multiplied by P(M).