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?

Question

Philoid · Accepted Answer

Let C represents the event that random family has colour television, W represents the event that family has black & white set and C ∩ W represents that they own both kind of sets.

According to question:

P(C) = 0.87

P(W) = 0.36 and P(C ∩ W) = 0.30

We need to find the probability of the event that a family owns either anyone kind of set.

i.e we need to find P(C or W) = P(C ∪ W) = ?

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

P(E ∪ F) = P(E) + P(F) – P(E ∩ F)

∴ P(C ∪ W) = P(C) + P(W) – P(C ∩ W)

⇒ P(C ∪ W) = 0.87 + 0.36 – 0.30 = 0.93