The probability that a student passes in Mathematics is 0.8 and the probability that he passes in English is 0.7. If the two events are independent, then the probability that the student passes in at least one of the two subjects is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0.94
“At least one pass” is the complement of “fails in both”. The failure probabilities are
\( P(\text{fails Mathematics}) = 1 - 0.8 = 0.2 \)
\( P(\text{fails English}) = 1 - 0.7 = 0.3 \)
The events are independent, so the probabilities multiply:
\( P(\text{fails both}) = 0.2 \times 0.3 = 0.06 \)
Hence
\( P(\text{at least one pass}) = 1 - 0.06 \)
\( = 0.94 \)
Why the other options are incorrect
Option (2) 0.56 — Incorrect. This is \(0.8 \times 0.7\), the probability of passing in both subjects.
Option (3) 0.38 — Incorrect. This is \(0.8 \times 0.3 + 0.2 \times 0.7\), the probability of passing in exactly one subject.
Option (4) 0.06 — Incorrect. This is the probability of failing in both subjects.