Question

The probability that a person will travel by plane is 3/5 and that he will travel by train is 1/4. What is the probability that he (she) will travel by plane or train?

Answer 1

Let T denotes the event that person travels by train and A denotes that event that person travels by plane 

Given, P(T) = \(\frac{3}{5}\)  and P(A) = \(\frac{1}{4}\)  

We need to find the probability that person travels by plane or train i.e. P(T or A) = P(T∪A) 

Note: By definition of P(A or B) under axiomatic approach(also called addition theorem) we know that:

P(A∪B) = P(A) + P(B) – P(A ∩ B) 

∴ P(T∪A) = P(T) + P(A) – P(A ∩ T) 

∵ A person can never travel with both plane and train simultaneously. 

∴ P(A∩T) = 0 

Hence, 

P(T∪A) = P(T) + P(A) =   \(\frac{3}{5}\)  + \(\frac{1}{4}\) = \(\frac{17}{20}\)