To determine the probability that the horse will win the race given the odds in favor are [tex]\(7:4\)[/tex], follow these steps:
1. Understand the Concept of Odds:
- Odds in favor of an event are the ratio of the number of ways the event can happen to the number of ways the event can fail to happen.
- Given the odds in favor of the horse winning are [tex]\(7:4\)[/tex], it means that for every 7 outcomes where the horse wins, there are 4 outcomes where the horse does not win.
2. Calculate the Total Number of Possible Outcomes:
- To find the total outcomes, sum the number of outcomes in favor of the horse winning and the number of outcomes against it.
- Here, the total outcomes [tex]\( = 7 + 4 = 11 \)[/tex].
3. Calculate the Probability:
- The probability of an event is the ratio of the number of successful outcomes to the total number of outcomes.
- In this case, the number of successful outcomes (i.e., the horse winning) is 7.
- Therefore, the probability [tex]\( P \)[/tex] that the horse will win is given by:
[tex]\[
P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{7}{11}
\][/tex]
Thus, the probability that the horse will win the race is [tex]\(\frac{7}{11}\)[/tex].
So, the correct answer is:
C. [tex]\(\frac{7}{11}\)[/tex]
