Question

a single die is rolled. find the odds in favor of rolling a number greater than 2.

the odds in favor of rolling a number greater than 2 are \\(\square:\square\\). (simplify your answers.)

Explanation:

Step1: Determine the number of favorable outcomes

When rolling a die, the sample space \(S=\{1,2,3,4,5,6\}\). The numbers greater than \(2\) are \(3\), \(4\), \(5\), \(6\). So the number of favorable outcomes \(n(F) = 4\).

Step2: Determine the number of unfavorable outcomes

The numbers not greater than \(2\) are \(1\), \(2\). So the number of unfavorable outcomes \(n(U)=2\).

Step3: Calculate the odds in favor

The formula for odds in favor is \(\text{Odds in favor}=\frac{n(F)}{n(U)}\). Substituting \(n(F) = 4\) and \(n(U)=2\), we get \(\frac{4}{2}\).

Answer:

\(2:1\)