Ex 13.2, 7 - Chapter 13 Class 12 Probability

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Ex 13.2, 7 Given that the events A and B are such that P(A) = 1﷮2﷯ , P (A ∪ B) = 3﷮5﷯ and P(B) = p. Find p if they are (i) mutually exclusive Given, P(A) = 1﷮2﷯ , P (A ∪ B) = 3﷮5﷯ and P(B) = p. Given sets A & B are mutually exclusive, So, they have nothing in common ∴ P(A ∩ B) = 0 We know that P(A ∪ B) = P(A) + P(B) – P(A ∩ B) Putting values 3﷮5﷯ = 1﷮2﷯ + p – 0 3﷮5﷯ – 1﷮2﷯ = p 6 − 5﷮10﷯ = p 1﷮10﷯ = p p = 𝟏﷮𝟏𝟎﷯ Ex 13.2, 7 Given that the events A and B are such that P(A) = 1﷮2﷯ , P (A ∪ B) = 3﷮5﷯ and P(B) = p. Find p if they are (ii) independent. Since events A & B are independent, So, P(A ∩ B) = P(A) P(B) = 1﷮2﷯ × p = 𝑝﷮2﷯ Now, P(A ∪ B) = P(A) + P(B) – P(A ∩ B) Putting values 3﷮5﷯ = 1﷮2﷯ + p – 𝑝﷮2﷯ 3﷮2﷯ – 1﷮2﷯ = p – 𝑝﷮2﷯ 6 − 5﷮10﷯ = 𝑝﷮2﷯ 1﷮10﷯ = 𝑝﷮2﷯ p = 2﷮10﷯ p = 𝟏﷮𝟓﷯