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Four candidates are seeking a vacancy on a school board. If A is twice as likely to be elected as B, and B and C are given about the same chance of being elected, while C is twice as likely to be elected as D, what are the probabilities that

C will win

User Pacemaker
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Final answer:

To find the probability that candidate C will win, we need to calculate the ratio of the probability of candidate C winning to the total probability of all candidates winning. Since candidate C is twice as likely to be elected as candidate D, the probability of candidate C winning is 2/6 or 1/3.

Step-by-step explanation:

To find the probabilities that candidate C will win, we need to consider the information given about the probabilities of the other candidates being elected. Let's assign a probability value to candidate D, let's say 1x. According to the information given, candidate C is twice as likely to be elected as candidate D, so we can assign a probability value of 2x to candidate C. Since candidate B and candidate C are given about the same chance of being elected, we can assign a probability value of 1x to candidate B. And since candidate A is twice as likely to be elected as candidate B, we can assign a probability value of 2x to candidate A.

Now, let's summarize the probabilities:

  • Candidate A: 2x
  • Candidate B: 1x
  • Candidate C: 2x
  • Candidate D: 1x

To find the probability that candidate C will win, we need to calculate the ratio of the probability of candidate C winning to the total probability of all candidates winning. Since there are four candidates in total, the total probability is 2x + 1x + 2x + 1x = 6x. Therefore, the probability that candidate C will win is 2x/6x = 2/6 = 1/3.

User Joe Strout
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