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  • 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

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?

Answers (1)

Let us consider that,

E1 be the element that a family owns a colour TV & E2 be the event that a family owns black & white TV.

Now P(E1) = 0.87 & P(E2) = 0.36 …….. (given)

& P (E1 ∩ E2) = 0.30

To find: probability that the family owns either anyone or both kinds of sets.

Now, by the general rule –

P (A U B) = P(A) + P(B) – P(A ∩ B)

We have,

 P (E1 U E2) = P(E1) + P(E2) – P(E1 ∩ E2)

                        = 0.87 + 0.36 – 0.30

                        = 1.23 – 0.30

                        = 0.93

Therefore, 0.93 is the required probability

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