question_answer 1)

A coin is tossed three times, where (i) E : head on third toss, F : heads on first two tosses (ii) E : at least two heads F : at most two heads (iii) E : at most two tails F: at least one tail Find P(E/F).  

Answer:

S = {HHH, HHT, HTH, THH,                         HTT, THT, TTH, TTT} (i)   E = {HHH, HTH, THH, TTH}       F = {HHH, HHT}       E  F = {HHH}                                                      (ii)   E = {HHH, HHT, HTH, THH}             F = HHT, HTH, THH, HTT,             THT, TTH, TTT}                         ;                         (i)     E = {HHH, HHT, HTH, THH, HTT, THH, TTH}       F = {HHT, HTH, THH, HTT, THT, TTH, TTT}       {HHT, HTH, THH, HTT, THT, TTH}