Mother, father and son line up at random for a family picture

E : son on one end, F : father in middle


Determine P(E|F)


Let M denote mother, F denote father and S denote son.

Then, the sample space for the given experiment will be:


S = {MFS, SFM, FSM, MSF, SMF, FMS}


Here, E: Son on one end


And F: Father in middle


E = {MFS, SFM, SMF, FMS} and F = {MFS, SFM}


E F = {MFS, SFM}


So,


Now, we know that


By definition of conditional probability,




P(E|F) = 1


9
1