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 anyone or both kinds of sets?

Answer 1

Let E₁ be the event that a family owns colour television set E₂ be the event that the family owns black and white television set.

Given that P(E₁) = 0.87, P(E₂) = 0.36

And P(E₁ ∩ E₂) = 0.30

∴ The probability that a family owns either colour television set or black and white television set

∴ P(E₁ ∪ E₂) = P(E₁) + P(E₂) – P(E₁ ∩ E₂)

= 0.87 + 0.36 – 0.30

= 0.93

Hence, the required probability = 0.93