Question

Mother, father and son line up at random for a family picture E: son on one end, F: father in middle

Answer 1

It is given that when three persons Mother (M), father (F) and son (S) line up, then possible sample space is 6.

s={ MFS,MSF,FMS,FSM,SFM,SMF }.

Let E be the event that son is at one end,

E={ MFS,FMS,SFM,SMF } P( E )= 4 6 = 2 3

Let F be the event that father is in middle,

F={ SFM,MFS } P( F )= 2 6 = 1 3

The common outcome between E and F is,

E∩F={ MFS,SFM } P( E∩F )= 2 6 = 1 3

The probability P( E|F ) is calculated as,

P( E|F )= P( E∩F ) P( F ) = 1 3 1 3 =1

Therefore, the value of P( E|F ) is 1.