Naman has to attend his friend's marriage. He can reach the wedding venue by train, bus or a…

Naman has to attend his friend's marriage. He can reach the wedding venue by train, bus or a two-wheeler. The probability of Naman using these as means of transport are $\frac{3}{10}$, $\frac{1}{5}$ and $\frac{1}{2}$ respectively. The probability of Naman reaching the wedding venue on time are $\frac{1}{4}$, $\frac{1}{3}$ and $\frac{2}{5}$ if he uses train, bus and two-wheeler respectively. Naman reached the venue late. What is the probability that he travelled by train?