SOLUTION: In a three-way race for the U.S. Senate, polls indicate that the two leading candidates are running neck-and-neck, while the third candidate is receiving one-third the support of e

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Question 346169: In a three-way race for the U.S. Senate, polls indicate that the two leading candidates are running neck-and-neck, while the third candidate is receiving one-third the support of each of the two front runners. Registered voters are chosen at random and asked which of the three will get their vote. What are the probabilities for for the events.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the support of one of the front runners.
The 3rd candidate is getting 2x/3 support
2x + 2x/3
= 6x/3 + 2x/3
=8x/3 total support.
.
x / 8x/3
= x * 3/8x
=3x/8x
=3/8 probability for either of the front runners winning.
.
2x/3 / 8x/3
= 2x/3 * 3/8x
=6x/24x
=1/4 probability of the 3rd candidate winning.
.
3/8 + 3/8 + 1/4 = 1
.
Ed