Let E 1 and E 2 be two events such that the conditional probabilities P E 1 ∣ E 2 = 1 2 , P E 2 ∣ E 1 = 3 4 and P E 1 ∩ E 2 = 1 8 . Then

Question

Let E 1 and E 2 be two events such that the conditional probabilities P E 1 ∣ E 2 = 1 2 , P E 2 ∣ E 1 = 3 4 and P E 1 ∩ E 2 = 1 8 . Then, P E 1 ∩ E 2 = P E 1 · P E 2, P E 1 ' ∩ E 2 ' = P E 1 ' · P E 2, P E 1 ∩ E 2 ' = P E 1 · P E 2, P E 1 ∪ E 2 = P E 1 P E 2

MARKS App · Accepted Answer

P E 1 ∩ E 2 P E 2 = 1 2 , P E 2 ∩ E 1 P E 1 = 3 4 , P E 1 ∩ E 2 = 1 8 ⇒ P E 2 = 1 4 , P E 1 = 1 6 , P E 1 ∪ E 2 = 1 6 + 1 4 - 1 8 = 7 24 P E ' ∩ E 2 ' = P E 1 ∪ E 2 ' = 1 - 7 24 = 17 24 P E 2 ' = 3 4 ⇒ P E 1 ∩ E 2 = P E 1 P E 2 ' P E 1 ∩ E 2 ' = P E 1 - P E 1 ∩ E 2 = 1 6 - 1 8 = 1 24 P E 1 ∩ E 2 ' = P E 1 · P E 2

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