Question

In a large metropolitan area, the probabilities are 0.87, 0.36, 0.30 that a family (randomly chosen for a sample survey) owns a colour television set, a black and white television set, or both kinds of sets. What is the probability that a family owns either any one or both kinds of sets?  

Answer 1

Let A be the event that a family owns a colour television set and B be the event that a family owns a black and white television set.
So, A ∩ B is the event that a family owns both a colour television set and a black and white television set.
∴ P(A) = 0.87, P(B) = 0.36 and P(A ∩ B) = 0.30            (Given)
Now,
P(a family owns either any one or both kinds of television sets)
= P(A ∪ B)
= P(A) + P(B) − P(A ∩ B)
= 0.87 + 0.36 − 0.30
= 0.93
Hence, the required probability is 0.93.