experts calculate the probability of a particular horse winning the kentucky derby to be $p(win)=0.2$. what…

Explanation:

Step1: Recall probability rule

The sum of the probability of an event occurring and not occurring is 1. Let $P(win)$ be the probability of winning and $P(not\ win)$ be the probability of not - winning. So $P(win)+P(not\ win)=1$.

Step2: Calculate $P(not\ win)$

Given $P(win) = 0.2$, then $P(not\ win)=1 - P(win)=1 - 0.2 = 0.8$.

Step3: Recall odds - against formula

The odds against an event $E$ is given by $\frac{P(\text{not }E)}{P(E)}$. Here, the event $E$ is the horse winning. So the odds against the horse winning is $\frac{P(not\ win)}{P(win)}$.

Step4: Calculate odds against

Substitute $P(not\ win)=0.8$ and $P(win)=0.2$ into the odds - against formula. $\frac{0.8}{0.2}=\frac{8}{2}=4$ to $1$.

Answer:

$P(not\ win)=0.8$ Odds against: 4 to 1