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Question
Determine P(E|F).
Mother, father and son line up at random for a family picture
E: son on one end, F: father in middle
Solution
Let m, f and s denote respectively the mother, father and the son, then sample space S is S = {mfs, msf, fms, fsm, smf, sfm),
E: son on one end
F: father in the middle
i.e., E = {mfs, fms, sfm, smf) and F = {sfm, mfs)
⇒ E ∩ F = {mfs, sfm)
`P (E) = 4/6 = 2/3, P (F) = 2/6 = 1/3, P (E cap F) = 2/6 = 1/3`
∴ `P (E|F) = (P (E cap F))/(P (F))`
`= (1/3)/(1/3) = 1`
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