Question:
In a large metropolitan area, the probabilities are .87, .36, .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?
Solution:
E1 = Event that a family owns colour television
E2 = Event that the family owns black and white television
Given that P (E1) = 0.87
P (E2) = 0.36 and P (E1 ⋂ E2) = 0.30
Now, we have to find the probability that a family owns either anyone or both kinds of sets.
By General Addition Rule, we have
P (A ∪ B) = P(A) + P(B) – P (A ∩ B)
∴ P (E1⋃ E2) = P (E1) + P (E2) – P (E1⋂ E2)
= 0.87 + 0.36 – 0.30
= 1.23 – 0.30
= 0.93
Hence, the required probability is 0.93