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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,

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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 anyone or both kinds of sets? Select the correct answer from above options

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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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