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?
Let T denotes the event that person travels by train and A denotes that event that person travels by plane
Given, P(T) = 3/5 and P(A) = 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) = 3/5 + 1/4 = 17/20