Question

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 18 horses. what is the probability of 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.)

Explanation:

Step1: Calculate the number of ways to choose 2 horses out of 18

We use the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 18$ and $r=2$. So $C(18,2)=\frac{18!}{2!(18 - 2)!}=\frac{18\times17\times16!}{2\times1\times16!}=\frac{18\times17}{2}= 153$.

Step2: Determine the probability

There is only 1 winning combination. The probability $P$ of winning is the number of favorable outcomes divided by the number of total outcomes. So $P=\frac{1}{153}\approx0.00654$.

Answer:

$0.00654$