NDA 2 2025 Maths, question 108

Topic: Probability

Q108Not scored: no correct option as printed

The probability that a student passes Physics test is $2/3$ and the probability that he passes both Physics test and English test is $11/15$ . The probability that he passes at least one test is $4/5$ . What is the probability that he passes English test?

(a) $11/15$
(b) $13/15$
(c) $14/15$
(d) $1$

Solution.

Not scored: no correct option as printed.

Answer: not scored. No option is correct as printed.

The data violate P(Physics∩English)≤P(Physics): 11/15>2/3=10/15.
Formal inclusion–exclusion would give P(English)=4/5−2/3+11/15=13/15, option (b), but it also exceeds the stated union probability 4/5.
Thus no valid probability model satisfies the source; (b) is only a mechanical, invalid-data result.