In a horse race, a particular bet is won if you selected the two horses that finish first and second, and they can be selected in any order. A certa winning this bet if you randomly select the horses? The possibility of winning this bet when randomly selecting the horses is (Round to five decimal places as needed.)

To determine the probability of winning the bet in the horse race scenario you've described, we need to know the total number of horses participating in the race. However, I'll outline the general approach to solving this problem, and you can apply it once the total number of horses is known. ### Problem Breakdown 1. **Total Number of Horses (n):** Let's denote the total number of horses in the race as \( n \). 2. **Selecting Two Horses:** You are selecting two horses out of the \( n \) to predict which ones will finish first and second, regardless of their order. 3. **Total Possible Outcomes:** The number of ways to choose 2 horses out of \( n \) is given by the combination formula: \[ \text{Total Combinations} = \binom{n}{2} = \frac{n(n-1)}{2} \] 4. **Favorable Outcomes:** There is only **one** favorable outcome where the two selected horses are exactly the ones that finish first and second (order doesn't matter). 5. **Probability Calculation:** The probability \( P \) of selecting the correct two horses is the ratio of favorable outcomes to total possible outcomes: \[ P = \frac{1}{\binom{n}{2}} = \frac{2}{n(n-1)} \] ### Example Calculation Suppose there are **10 horses** in the race (\( n = 10 \)). 1. **Total Combinations:** \[ \binom{10}{2} = \frac{10 \times 9}{2} = 45 \] 2. **Probability:** \[ P = \frac{1}{45} \approx 0.02222 \] Rounded to five decimal places, the probability is **0.02222**. ### General Formula If you provide the total number of horses \( n \), you can use the formula below to find the probability: \[ P = \frac{2}{n(n-1)} \] **Please provide the total number of horses in the race** so that I can compute the exact probability for your specific case.