Define an event A = {HHH, TTT, HTH} and an event B = {HHH, HTH, HHT, TTH}. Compute P(A) and P(B).

1. Define an event A = {HHH, TTT, HTH} and an event B = {HHH, HTH, HHT, TTH}. Compute P(A) and P(B).
2. Compute P(A B).
3. Compute P(B A).
4. Are events A and B independent?
5. Are events A and B mutually exclusive?

A = { HHH, TTT, HTH }, B = { HHH, HTH, HHT, TTH }

∴ A∩B = { HHH, HTH }

∴ n(A) = 3, n(B) = 4, n(A∩B) = 2

Also n(S) = 2³ = 8.

∴ P(A) = n(A) / n(S) = 3/8 ........................................… (1)

... P(B) = n(B) / n(S) = 4/8 = 1/2 ........................................… (2)

∴ P(A∩B) = P(B∩A) = n(A∩B) / n(S) = 2/8 = 1/4 ................. (3)

... P(A|B) = n(A∩B) / n(B) = 2/4 = 1/2 .................................... (4)

... P(B|A) = n(A∩B) / n(A) = 2/3 ........................................… (5)
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... P(A)·P(B) = (3/8)(1/2) = 3/16 ≠ P(A∩B)

∴ A and B are Not Independent ........................................… (6)
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Also : A∩B ≠ Φ

∴ A, B are Not Mutually Exclusive either ............................... (7)
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