Question

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

Answer 1

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)=(3)/(6) \\ =(1)/(2) \end{gathered}`

Probability of rolling a number less than 4 becomes

`\begin{gathered} Pr(less\text{ than 4\rparen = }(3)/(6) \\ =(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} =(2)/(6) \\ =(1)/(3) \end{gathered}`

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

`\begin{gathered} (1)/(2)+(1)/(2)-(1)/(3) \\ (3+3-2)/(6) \\ =(4)/(6) \\ =(2)/(3) \end{gathered}`

Hence the answer is 2/3