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 certain horse race had a field of 17 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, let's break down the problem step by step. ### **Understanding the Bet:** - **You win the bet** if you correctly select the two horses that finish **first and second**, regardless of the order in which they finish. - **Total horses in the race:** 17 ### **Calculating the Probability:** 1. **Total Possible Outcomes for First and Second Place:** - **First place:** 17 possible horses. - **Second place:** 16 remaining horses. - **Total ordered outcomes:** \( 17 \times 16 = 272 \) 2. **Favorable Outcomes:** - Since the order doesn't matter (i.e., your two selected horses can finish first and second in any order), there are **2 favorable outcomes** for your chosen pair: - Horse A finishes first and Horse B finishes second. - Horse B finishes first and Horse A finishes second. 3. **Probability Calculation:** \[ \text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Possible Outcomes}} = \frac{2}{272} = \frac{1}{136} \approx 0.00735 \] ### **Final Answer:** The probability of winning the bet when randomly selecting the two horses is **0.00735**. **Answer:** The probability of winning the bet is 0.00735