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Question
Determine P(E|F).
A coin is tossed three times, where
E: at most two tails, F: at least one tail
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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: at most two tails = {HTT, THT, TTH, HHT, HTH, THH, HHH}
F: at least one tail = {THH, HTH, HHT, TTH, THT, HTT, TTT}
∴ E ∩ F = {HHT, HTT, HTH, THH, THT, TTH}
E ∩ F = `6/8`, P(F) = `7/8`
`P(E|F) = (P(E ∩ F))/(P(F))`
`= (6/8)/(7/8)`
`= 6/7`
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