Question

Determine P(E|F).

A coin is tossed three times, where

E: at most two tails, F: at least one tail

Answer 1

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`