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