At first:

Table `X`: `A AB`

Table `Y`: `AB`

Let

P(AX) = probability of selecting `A` from `X`

P(BX) = probability of selecting `B` from `X`

P(BY) = probability of selecting `B` from `Y`

`P(B_Y) = P(A_X) times P(B_Y|A_X) +` ` P(B_X) times P(B_Y|B_X)`

`=2/3 times 1/3 + 1/3 times 2/3`

`=4/9`

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