Question

experts calculate the probability of a particular horse winning the kentucky derby to be $p(win)=0.3$. 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: Calculate probability of not - winning

The sum of the probability of an event happening and the probability of it not happening is 1. Let $P(win) = 0.3$. Then $P(not\ win)=1 - P(win)$.
$P(not\ win)=1 - 0.3=0.7$

Step2: Calculate odds against winning

The odds against an event $E$ is given by the ratio of the probability of the event not occurring to the probability of the event occurring.
Odds against winning $=\frac{P(not\ win)}{P(win)}$.
We know $P(not\ win) = 0.7$ and $P(win)=0.3$. So odds against winning $=\frac{0.7}{0.3}=\frac{7}{3}$, which means 7 to 3.

Answer:

$P(not\ win)=0.7$
Odds against winning: 7 to 3