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Question
Mother, father and son line up at random for a family photo. If A and B are two events given by
A = Son on one end, B = Father in the middle, find P(B / A).
Solution
If the mother (M), father (F), and son (S) line up for the family picture, then the sample space will be
A → Son on one end.
B → Father in the middle
Son (s) , Father (F), Mother (M)
Total possible cases.
S = {MFS, MSF, FMS, FSM, SMF, SFM}
A= {MFS, FMS, SMF, SFM}
B = {MFS, SFM}
∴ A ∩ B = {MFS, SFM}
`P(A) = 4/6 = 2/3 P (A cap B ) = 2/6 = 1/3`
` P(B) = 2/6 = 1/3`
`P(B/A) = (P(A cap B))/(P(A)) = (1/3)/(2/3) = 1/2`
`P(B/A) = 1/2 `
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