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? [NCERT EXEMPLAR]

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.