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Question
Determine P(E|F).
A coin is tossed three times, where
E: head on third toss, F: heads on first two tosses
Solution
If a coin is tossed three times, then the sample space 'S' is,
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Total sample space = 23 = 8.
E = {HHH, HTH, THH, TTH}
F = {HHH, HHT}
E ∩ F = {HHH}
P(E ∩ F) = `1/8`, P(F) = `2/8 = 1/4`
P(E | F) = `(P(E ∩ F))/(P(F)) = (1/8)/(1/4)`
`= 4/8`
`= 1/2`
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