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Conditional Probability - Values given
Last updated at May 25, 2021 by Teachoo
Ex 13.1, 4 Evaluate P(A ∪ B), if 2P(A) = P(B) = 513 and P(A|B) = 25 Given, 2P(A) = P(B) = 513 So, P(A) = 12 × 513 = 526 & P(B) = 513 Also, P(A|B) = 25 We know, P(A|B) = 𝑃(𝐴 ∩ 𝐵)𝑃(𝐵) 25 = 𝑃(𝐴 ∩ 𝐵) 513 P(A ∩ B ) = 25 × 513 P(A ∩ B ) = 𝟐𝟏𝟑 Also, P(A ∪ B) = P(A) + P(B) – P(A ∩ B) = 526 + 513 - 2 13 = 526 + 313 = 526 + 626 = 1126 ∴ P(A ∪ B) = 𝟏𝟏𝟐𝟔