A candidate has to go to the examination…

Single correct+4 / -1Answer matches NTA’s final key

A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation for the entire distance out of bus, scooter and car. The probabilities of the candidate going by bus, scooter and car, respectively, are $\frac{2}{5}$ , $\frac{1}{5}$ and $\frac{2}{5}$ . The probabilities that the candidate reaches late at the examination centre are $\frac{1}{5}$ , $\frac{1}{3}$ and $\frac{1}{4}$ if the candidate uses bus, scooter and car, respectively. Given that the candidate reached late at the examination centre, the probability that the candidate travelled by bus is:

$\frac{11}{37}$
$\frac{12}{37}$
$\frac{13}{37}$
$\frac{14}{37}$

Solution

This is Bayes' theorem. Let $L$ be "reached late".

$P(L) = \tfrac25 \cdot \tfrac15 + \tfrac15 \cdot \tfrac13 + \tfrac25 \cdot \tfrac14 = \tfrac{2}{25} + \tfrac{1}{15} + \tfrac{1}{10} = \tfrac{12 + 10 + 15}{150} = \tfrac{37}{150}.$

$P(\text{bus} \mid L) = \frac{2/25}{37/150} = \frac{12/150}{37/150} = \frac{12}{37}.$

Answer: $\frac{12}{37}$ .

Answer checked against the official answer key. The solution is our own working.

JEE MAIN 2026 · Statistics and Probability

Solution

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