In the family mother, father and son stand up at random for a family picture.
Define following two events :
E = [Son stands at one of the two ends in the picture]
F = [Father stands in the middle of the picture]
The value of P(F/E) is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{1}{2}\)
Let M, F and S stand for mother, father and son. The three can stand in 3! = 6 equally likely orders:
MFS, MSF, FMS, FSM, SMF, SFM
The son is at an end in MFS, FMS, SMF and SFM, so n(E) = 4.
The father is in the middle in MFS and SFM. In both the son is at an end, so \(n(E \cap F) = 2\).
By conditional probability,
\( \displaystyle P(F/E) = \frac{n(E \cap F)}{n(E)} = \frac{2}{4} = \frac{1}{2} \)