Question
If the odds against Deborah's winning first prize in a chess tournament are 2 to 11 , what is the probability of the event that she will win first prize? The probability that Deborah will win first place is \( \square \). (Type an integer or a fraction.)
Ask by Chen Tyler. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The probability that Deborah will win first prize is \( \frac{11}{13} \).
Solution
The odds against Deborah winning the first prize are given as 2 to 11. This means for every 2 ways she does not win, there are 11 ways she does win.
To find the probability that Deborah wins first prize:
1. **Total possible outcomes** = 2 (failures) + 11 (successes) = 13
2. **Probability of winning** = Number of successes / Total outcomes = \( \frac{11}{13} \)
So, the probability that Deborah will win first prize is \( \frac{11}{13} \).
**Answer:** \( \frac{11}{13} \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find the probability of Deborah winning first prize given the odds against her winning are 2 to 11, we can use the formula for probability based on odds. The odds against winning are the ratio of the number of ways she can lose to the number of ways she can win. In this case, for every 2 ways she can lose, there are 11 ways she can win. So, the total outcomes = 2 (losing) + 11 (winning) = 13. The probability \( P \) of winning is given by the number of winning outcomes divided by the total outcomes: \[ P(\text{win}) = \frac{11}{13} \] Thus, the probability that Deborah will win first place is \( \frac{11}{13} \).
