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Answer the following probability problems:

1) The odds against Buttermilk winning the Triple Crown in horse racing are 82:3. Find the probability that Buttermilk wins the Triple Crown.

Sagot :

GinnyAnsweridn
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%.
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