Question

A single, six sided die is rolled. Find the probability of rolling an odd number or a number less than 4

Answer 1

SOLUTION

The odd numbers in a six sided die are 1, 3 and 5. That is 3 numbers

The numbers less than four are 1, 2 and 3. That is 3 numbers

The probability of rolling an odd number becomes

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

Probability of rolling a number less than 4 becomes

$\begin{gathered} Pr(less\text{ than 4\rparen = }\frac{3}{6} \\ =\frac{1}{2} \end{gathered}$

Now looking at the odd numbers and the numbers less 4, we have

1, 3, 5 and 1, 2, 3. So between these numbers are 1 and 3. which is 2. Probability of this is

$\begin{gathered} =\frac{2}{6} \\ =\frac{1}{3} \end{gathered}$

Hence the probability of rolling an odd number or a number less than 4 becomes

$\begin{gathered} \frac{1}{2}+\frac{1}{2}-\frac{1}{3} \\ \frac{3+3-2}{6} \\ =\frac{4}{6} \\ =\frac{2}{3} \end{gathered}$

Hence the answer is 2/3