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Question
Determine P(E|F).
A coin is tossed three times, where
E: at least two heads, F: at most two heads
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: Minimum two heads: {HHH, HTH, THH, HHH}
F: At most one head : P(E ∩ F) = `"Number of events occurring"/"Total number"`
= {TTT, HTT, THT, HTT, HHT, HTH, THH}
∴ E ∩ F = {HHT, HTH, THH}
Hence, `P (E) = 4/8 = 1/2, P(F) = 7/8`
and `P (E cap F) = 3/8`
P(E | F) = `(P(E ∩ F))/(P(F))`
`= (3/8)/(7/8)`
= `3/7`
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