Question

Determine P(E|F).

A coin is tossed three times, where

E: head on third toss, F: heads on first two tosses

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 = {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`