In a certain election, the incumbent Republican will run against the Democratic nominee. There are three Democratic candidates, D1, D2 and D3, whose chances of gaining the Democratic nomination are .50, .35 and .15, respectively. Here are the chances that the Republican will win against each of these possible Democratic nominees:

Question

vs. D1: 0.60 vs. D2: 0.50 vs. D3: 0.40

(a) Name (but do not give) the probability formula that is needed to find the chance that the Republican will win the election.

(b) Find the probability that the Republican will win the election.
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Im not sure how to start.

Answer 1

a
two rules -addition rule (special case for mutually exclusive events) and multiplication rule (for independent events)
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b
probability of winning against D1 = probability of D1 being nominee * probability of Beating D1 if nominee
= .5 *.6 = .3
same multiply for candidate D2
= .35 * .5 = .175
same for D3
.15 * .4 = .06
now chances of winning = sum - any intersections but there are no intersections, only one democratic candidate in the end so = .3+.175+.06 = .535