Answer 1

We have two events such that
A = a person will travel by plane
and B = a person will travel by train.
i.e. 

\[P\left( A \right) = \frac{3}{5}\]  and \[P\left( B \right) = \frac{1}{4}\]

Since A and B are mutually exclusive events, we have:
P (A ∩ B) = 0
By addition theorem, we have:
P (A ∪ B) = P(A) + P (B) - P (A ∩ B)
                =  \[\frac{3}{5} + \frac{1}{4} - 0 = \frac{12 + 5}{20} = \frac{17}{20}\]
Hence, required probability = \[\frac{17}{20}\]