In a large metropolitan area, the probabilities are .87, .36, .30

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

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