Question

The numbers $1$ to $10$ are printed on $10$ counters and mixed in a bag. Find the probability that a counter picked at random is an odd number.

Answer 1

Step 1 Finding the favorable and total outcomes:

There are $10$ counters placed in a bag, so the total number of outcomes is $10$.

Odd numbers are the numbers that are not divisible by $2$.

In the range $1$ to $10$, the numbers which are not divisible by $2$ are:

$1,3,5,7,9$

So the number of favorable outcomes is $5$.

Step 2 Finding the probability that the drawn counter is odd:

The formula for the probability is expressed as,

$Probability=\frac{Number of favorable outcomes}{Total number of outcomes}$

Substitute favorable number of outcomes as $5$ and the total number of outcomes as $10$.

$$\begin{gathered} \Rightarrow P\left(oddnumber\right)=\frac{5}{10} \\ \therefore P\left(oddnumber\right)=\frac{1}{2} \end{gathered}$$

Hence, the probability of odd numbered counter from a bag of $10$ counters numbered $1$ to $10$ is $\frac{1}{2}$.