Certainly! Let's determine the probability that Buttermilk wins the Triple Crown, given the odds against Buttermilk winning are 82:3.
1. Understanding the Odds:
- The odds against Buttermilk winning are given as 82:3.
- This means there are 82 unfavorable outcomes for every 3 favorable outcomes.
2. Identifying Favorable and Unfavorable Outcomes:
- Favorable outcomes: 3 (the chances of Buttermilk winning)
- Unfavorable outcomes: 82 (the chances of Buttermilk not winning)
3. Calculating the Total Number of Outcomes:
- Total outcomes = Favorable outcomes + Unfavorable outcomes
- Total outcomes = 3 + 82 = 85
4. Finding the Probability:
- Probability of winning = (Number of favorable outcomes) / (Total number of outcomes)
- Probability of winning = 3 / 85
5. Simplifying the Probability:
- Probability of winning = 0.03529411764705882 (approximately)
Therefore, the probability that Buttermilk wins the Triple Crown is approximately 0.0353 or about 3.53%.
