Ex 13.1, 4 - Chapter 13 Class 12 Probability (Term 2)

Transcript

Ex 13.1, 4 Evaluate P(A ∪ B), if 2P(A) = P(B) = 5﷮13﷯ and P(A|B) = 2﷮5﷯ Given, 2P(A) = P(B) = 5﷮13﷯ So, P(A) = 1﷮2﷯ × 5﷮13﷯ = 5﷮26﷯ & P(B) = 5﷮13﷯ Also, P(A|B) = 2﷮5﷯ We know, P(A|B) = 𝑃(𝐴 ∩ 𝐵)﷮𝑃(𝐵)﷯ 2﷮5﷯ = 𝑃(𝐴 ∩ 𝐵)﷮ 5﷮13﷯﷯ P(A ∩ B ) = 2﷮5﷯ × 5﷮13﷯ P(A ∩ B ) = 𝟐﷮𝟏𝟑﷯ Also, P(A ∪ B) = P(A) + P(B) – P(A ∩ B) = 5﷮26﷯ + 5﷮13﷯ - 2﷮ 13﷯ = 5﷮26﷯ + 3﷮13﷯ = 5﷮26﷯ + 6﷮26﷯ = 11﷮26﷯ ∴ P(A ∪ B) = 𝟏𝟏﷮𝟐𝟔﷯