Question

The probability that a company executive will travel by plane is (2/5) and that he will travel by train is (1/3). Find the probability of his travelling by plane or train.

Answer 1

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) =  \(\frac{11}{15}\)