the odds against a particular candidate winning an election are estimated to be 4 to 19 if those odds are accurate what is the probability that that candidate will win the election
To determine the probability that the candidate will win the election, we need to convert the odds into a probability.
Let's consider the odds against the candidate winning, which are 4 to 19. This means that for every 4 favorable outcomes (candidate wins), there are 19 unfavorable outcomes (candidate loses).
To convert this into a probability, we need to find the total number of possible outcomes (favorable + unfavorable).
Total outcomes = favorable outcomes + unfavorable outcomes = 4 + 19 = 23
Now, we can calculate the probability of the candidate winning the election:
Probability of the candidate winning = favorable outcomes / total outcomes
Probability of the candidate winning = 4 / 23
Thus, the probability that the candidate will win the election, based on the given odds, is approximately 0.174 or 17.4%.
To find the probability of a candidate winning the election, we can use the odds ratio. The odds ratio is calculated as:
Odds ratio = Odds against winning / Odds in favor of winning
In this case, the odds against the candidate winning are 4 to 19. Therefore, the odds in favor of winning would be the inverse of the odds against winning, which is 19 to 4.
Now, let's calculate the probability using the odds ratio:
Probability of winning = Odds in favor of winning / (Odds in favor of winning + 1)
Plugging in the values, we have:
Probability of winning = (19 / 4) / (19 / 4 + 1)
= 19 / (19 + 4)
= 19 / 23
Therefore, the probability that the candidate will win the election is approximately 0.826 or 82.6%.