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If the odds on a bet are 50:1 against, what is the probability of winning? Express your answer as a fraction.

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To determine the probability of winning given the odds of 50:1 against, follow these steps:

1. Understand the odds: The odds of 50:1 against imply that for every 51 total outcomes, only 1 outcome results in a win while 50 outcomes result in a loss.

2. Translate the odds into probability:
- The total number of possible outcomes is the sum of both winning and losing scenarios.
- In this case, there is 1 way to win and 50 ways to lose, making a total of [tex]\(1 + 50 = 51\)[/tex] possible outcomes.

3. Calculate the probability:
- Probability is calculated as the number of favorable outcomes (winning in this case) divided by the total number of possible outcomes.
- Number of favorable outcomes for winning = 1.
- Total number of possible outcomes = 1 (win) + 50 (lose) = 51.

4. Form the fraction:
- Therefore, the probability of winning is the ratio of the number of winning outcomes to the total outcomes, which is [tex]\(\frac{1}{51}\)[/tex].

In conclusion, the probability of winning given the odds of 50:1 against is [tex]\(\frac{1}{51}\)[/tex].
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