Question

experts calculate the probability of a particular horse winning the kentucky derby to be $p(win)=0.8$. what is the probability (in decimal form) that the horse will not win the race? $p(not win)=square$ what are the odds against the horse winning the race? $square$ to $square$ simplify your answers.

Explanation:

Step1: Recall probability rule

The sum of the probability of an event happening and not - happening 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 $P(win) = 0.8$, then $P(not\ win)=1 - P(win)=1 - 0.8=0.2$.

Step3: Recall odds 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 the race.

Step4: Calculate odds against winning

We know $P(win)=0.8$ and $P(not\ win)=0.2$. The odds against the horse winning is $\frac{P(not\ win)}{P(win)}=\frac{0.2}{0.8}=\frac{1}{4}$, which means 1 to 4.

Answer:

$P(not\ win)=0.2$
Odds against winning: 1 to 4