Step 1 :The problem is asking for the probability of winning a trifecta bet in a horse race with 13 horses. A trifecta bet requires correctly predicting the first, second, and third place horses in the correct order.
Step 2 :Since the order matters, this is a permutation problem. The total number of possible outcomes is the number of ways to arrange 3 horses out of 13, which is a permutation of 13 items taken 3 at a time, denoted as P(13,3).
Step 3 :The number of successful outcomes is 1, because there is only one correct order of the first, second, and third place horses.
Step 4 :The probability of a successful outcome is the number of successful outcomes divided by the total number of outcomes.
Step 5 :Let's calculate this probability. The total number of outcomes is 1716 and the number of successful outcomes is 1.
Step 6 :So, the probability is \(\frac{1}{1716}\) which is approximately 0.0005827505827505828.
Step 7 :Final Answer: The probability that you will win the trifecta bet is approximately \(\boxed{0.0005827505827505828}\).