Question

Determine P(E|F).

A coin is tossed three times, where 

E: at least two heads, F: at most two heads

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: 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`