Question

experts calculate the probability of a particular horse winning the kentucky derby to be ( p(\text{win}) = 0.3 ).
what is the probability (in decimal form) that the horse will not win the race? ( p(\text{not win}) = )
what are the odds against the horse winning the race? to
simplify your answers.

Explanation:

Step1: Calculate the probability of not winning

The sum of the probability of an event happening and not happening is \(1\). So \(P(\text{not win})=1 - P(\text{win})\).
Given \(P(\text{win}) = 0.3\), then \(P(\text{not win})=1 - 0.3\).

Step2: Calculate the odds against winning

The odds against an event \(E\) is given by \(\frac{P(\text{not }E)}{P(E)}\).
Here \(P(\text{win}) = 0.3\) and \(P(\text{not win})=0.7\). The odds against winning is \(\frac{0.7}{0.3}=\frac{7}{3}\), which means \(7\) to \(3\).

Answer:

\(P(\text{not win}) = 0.7\)
The odds against the horse winning the race is \(7\) to \(3\)