The odds in favor of the horse winning a race are given as 9:5. Let's understand what this means and how to find the probability of the horse winning.
1. Interpret the Odds:
- The odds in favor are 9:5.
- This means that for every 9 favorable outcomes (the horse wins), there are 5 unfavorable outcomes (the horse does not win).
2. Calculate the Total Number of Outcomes:
- To find the total number of possible outcomes, add the number of favorable outcomes to the number of unfavorable outcomes:
[tex]\[
\text{Total outcomes} = 9 + 5 = 14
\][/tex]
3. Calculate the Probability:
- Probability is given by the ratio of favorable outcomes to the total number of outcomes.
- Thus, the probability that the horse will win the race is:
[tex]\[
\text{Probability of winning} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{9}{14}
\][/tex]
4. Choose the Correct Answer:
- Comparing this with the provided options, the correct answer is:
[tex]\[
\boxed{\frac{9}{14}}
\][/tex]
Therefore, the probability that the horse will win the race is [tex]\( \frac{9}{14} \)[/tex], which corresponds to option C.
