let A denote the event that a company executive will travel by plane and B denote the event of him travelling by train
Given : P(A) = \(\frac{2}{5}\), P(B) = \(\frac{1}{3}\)
To find : Probability of a company executive will be travelling by plane or train = P(A or B)
Formula used : P(A or B) = P(A) + P(B) - P(A and B)
Probability of a company executive will be travelling in both plane and train =P(A and B)= 0
(as he cannot be travelling by plane and train at the same time)
P(A or B) = \(\frac{2}{5}\) + \(\frac{1}{3}\) – 0
P(A or B) = \(\frac{6+5}{15}\) = \(\frac{11}{15}\)
P(A or B) = \(\frac{11}{15}\)
Probability of a company executive will be travelling by plane or train= P(A or B) = \(\frac{11}{15}\)