2 The voters in a large city are 40% white, 40% black, and 20% Hispanic. A black

Question

2 The voters in a large city are 40% white, 40% black, and 20% Hispanic. A black mayoral candidate anticipates attracting 30% of the white vote, 90% of the black vote, and 50% of the Hispanic vote. Draw a tree diagram with probabilities for the race (white, black, or Hispanic) and vote (Yes or No for the candidate) of a randomly chosen voter. I've started it for you White Black Hispanic Percent of overall vote candidate expects to get If a voter voted for the black mayoral candidate, what's the probability that he/she was also black? for the following conditional probability: P(BY) page That's the same as asking where Y-Voted For, B- Black. Use the equation" at the top of the calculate it

Explanation / Answer

let W, B and H represent voter is White; Black and Hispanic and Y represent voted for,

% of vote P(Y) =P(W)*P(Y|W)+P(B)*P(Y|B)+P(H)*P(Y|H)=0.4*0.3+0.4*0.9+0.2*0.5 =0.58 ~ 58.0%

P(B|Y) =P(B)*P(Y|B)/P(Y) =0.4*0.9/0.58 =0.62069

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