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.