Question

What are the odds in favor of rolling an odd number on a fair die?

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the number of odd numbers on a die

$\begin{gathered} \text{Odd number}=1,3,5 \\ n(odd)=3 \\ Total\text{ outcome of a die}=1,2,3,4,5,6 \\ n(Total)=6 \end{gathered}$

STEP 2: Find the probability of getting an odd number

$Pr(odd)=\frac{3}{6}=\frac{1}{2}$

STEP 3: Calculate the odd in favor

$\begin{gathered} odds\text{ in favour}=\frac{Pr(odd)}{1-Pr(odd)} \\ =\frac{\frac{1}{2}}{1-\frac{1}{2}}=\frac{\frac{1}{2}}{\frac{1}{2}}=\frac{1}{2}\div\frac{1}{2}=\frac{1}{2}\times\frac{2}{1}=1 \end{gathered}$

Hence, the odds in favorof rolling amn odd number on a fair die is 1