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Taylor, Moore, and Jenkins are candidates for public office. It is estimated that Moore and Jenkins have about the same probability of winning, and Taylor is believed to be twice as likely to win as either of the others. Find the probability of each candidate winning the election.

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Answer:

Taylor = 50%

Moore = 25%

Jenkins = 25%

Step-by-step explanation:

Assuming there are no other candidates and that someone has to win the election, the probabilities of Taylor, Moore, and Jenkins winning the election must add up to 1 or 100%.

[tex]T+M+J = 1\\[/tex]

Since Moore and Jenkins have about the same probability of winning, and Taylor is believed to be twice as likely to win as either of the others:

[tex]M=J\\T=2J\\J+J+2J=1\\J=0.25\\M=J=0.25\\T=2*0.25=0.5[/tex]

Taylor has a probability of 50% of winning the election.

Moore has a probability of 25% of winning the election.

Jenkins has a probability of 25% of winning the election.

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