Question

The probability that a company executive will travel by train is 2/3 and that he will travel by plane is 1/5. The probability of his travelling by train or plane is:
A. 2/15
B. 13/15
C. 15/13
D. 15/2

Answer 1

Hint: Use the relation between the probability of occurrence of either of the events with their individual probabilities and the probability if both occur simultaneously.

Complete step-by-step answer:
Given, the probability that a company executive will travel by train is 2/3 and that he will travel by plane is 1/5
Let the probability that a company executive will travel by train is given by \[P(T) = \dfrac{2}{3}\]
And the probability that a company executive will travel by plane is given by \[P(P) = \dfrac{1}{5}\]
Now, the probability that a company executive will travel by both train and plane is given by \[P(T \cap P)\]
Now, \[P(T \cap P) = 0\] as it is impossible for a person to travel both by train and plane simultaneously.
Now, the probability that a company executive will travel by train or plane is given by \[P(T \cup P)\]
Now, \[P(T \cup P) = P(T) + P(P) - P(T \cap P)\]
\[ \Rightarrow P(T \cup P) = \dfrac{2}{3} + \dfrac{1}{5} - 0\]
\[ \Rightarrow P(T \cup P) = \dfrac{{13}}{{15}}\]
Therefore, option (B) 13/15 is correct.

Note: Whenever we need to find the probability of occurrence of either of the 2 events then one should find the union of the probabilities of the 2 events and in case of the occurrence of both the events together has been asked then one should find the intersection of the 2 probabilities.