InterviewSolution
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InterviewSolution
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The probability that the tax-limit for income of males increases in the budget of a year is 0.66 and the probability that the tax- limit increases for income of females is 0.72. The probability that the tax-limit increases for income of both the males and females is 0.47. Find the probability that(i) the tax-limit increases for income of only one of the two, males and females,(ii) the tax-limit does not increase for income of males as well as females in the budget of that year. |
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Answer» A = Event that the tax-limit for income of males increases. B = Event that the tax-limit for income of females increases. A ∩ B = Event that the tax-limit for income of male and female increases. Here, P(A) = 0.66, P(B) = 0.72 and P(A ∩ B) =0.47 are given. (i) C = Event that the tax-limit increases only for one of the two male and female. A ∩ B’ = Event that the tax-limit increases for the income of male only and not of female OR A’ ∩ B = Event that the tax-limit increases for the income of female only and not of male Events A ∩ B’ and A’ ∩ B are mutually exclusive, ∴ P(C) = P(A ∩ B’) + P(A’ ∩ B) = [P(A) – P(A ∩ B)l + (P(B) – P(A ∩ B)] = [0.66 – 0.47] + [0.72 – 0.47] = 0.19 + 0.25 = 0.44 (ii) A’ ∩ B’ = Event that the tax-limit does not increase for income of either male or female. Now, P(A ∪ B) = P(A) + P(B) – P(A ∩ B) = 0.66 + 0.72 – 0.47 = 0.91 ∴ P(A’ ∩ B’) = P(A ∪ B)’ = 1 – P(A ∪ B) = 1 – 0.91 = 0.09 |
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