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 the bet when randomly selecting the horses is
(round to five decimal places as needed.)

Explanation:

Step1: Calculate total number of ways to select 2 horses out of 18

The number of combinations of choosing 2 horses out of 18 is given by 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 number of winning combinations

There is only 1 winning combination (the two horses that finish first and second).

Step3: Calculate the probability

The probability $P$ of winning is the number of favorable outcomes divided by the number of total outcomes. So $P=\frac{1}{153}\approx0.0065$.

Answer:

$0.0065$