Question

the probability of winning a prize in a local contest is \\( \frac { 1 } { 6 } \\). find the actual odds against winning a prize. (1 point)
1:5
6:1
5:1
1:6

Explanation:

Step1: Calculate the probability of not winning

The probability of winning \( P(W)=\frac{1}{6} \). The probability of not winning \( P(\overline{W})=1 - P(W)=1-\frac{1}{6}=\frac{5}{6} \).

Step2: Calculate the odds against winning

The formula for odds against an event \( E \) is \( \frac{P(\overline{E})}{P(E)} \). Here, odds against winning \(=\frac{P(\overline{W})}{P(W)}=\frac{\frac{5}{6}}{\frac{1}{6}}=\frac{5}{1}=5:1\).

Answer:

C. \( 5:1 \)