# The probability that a company executive will travel by plane is (2/5) and that he will travel by train is (1/3).

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.

Solution:

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 $=\mathrm{P}(\mathrm{A}$ or $\mathrm{B})=\frac{11}{15}$