please help!

[kennynguyen45]

There is an electoral vote. In Town X, 35% vote for person A and 20% vote for person B. In town Y, 25% vote for A and 30% vote for B. If all the votes for town X and Y are split between 2 random piles and a pile is chosen randomly, what is the probability that that if two votes are chosen from the pile that it will contain one vote for A and one vote for B

 

[Deleted member 4993]

There is an electoral vote. In Town X, 35% vote for person A and 20% vote for person B. In town Y, 25% vote for A and 30% vote for B. If all the votes for town X and Y are split between 2 random piles and a pile is chosen randomly, what is the probability that that if two votes are chosen from the pile that it will contain one vote for A and one vote for B

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[HallsofIvy]

"All the votes for town X and Y are split between 2 random piles" is very ambiguous! It sounds like all of the votes are mixed together and then divided randomly into two piles. But if that were the case, it would be impossible to answer the question. Instead I suspect it means that the votes from "town X" are put in one pile and the votes from "town Y" were put in another. There is a probability 1/2 that the votes from "town X" are chosen and 1/2 that the votes from "town Y" are chosen.

Suppose "town X" is chosen. We are told that "35% vote for person A and 20% vote for person B" so the probability that the two votes chosen are "AB" is 0.35*0.20= 0.07 and that the two votes are "BA" is 0.20*0.35= 0.07. The probability that one vote is for A and the other for B is 2*0.07= 0.14. Since there is a 1/2 probability that "town X" is chosen, multiply that by 1/2.

Suppose "town Y" is chosen. We are told that " 25% vote for A and 30% vote for B". So now what is the probability that the two votes are for A and B? Since there is a 1/2 probability that "town Y" is chosen, multiply that by 1/2.

Finally, add those two.