Question

A dice is thrown $20$ times and the outcomes are noted as shown below:

$\begin{array}{ccccccc}\text{Out comes}& 1& 2& 3& 4& 5& 6\\ \text{No. of times}& 2& 3& 4& 4& 3& 4\end{array}$

Now a dice is thrown at random, find the probability of getting:

ii. A number less than $3$

Answer 1

Find the probability of getting a number less than $3$

Given:

Total number of possible outcomes $=20$

Number less than $3$ are $2$ and $1$

$\begin{array}{ccccccc}\text{Out comes}& 1& 2& 3& 4& 5& 6\\ \text{No. of times}& 2& 3& 4& 4& 3& 4\end{array}$

From the table,
Number of times $2$ occurred $=3$
Number of times $1$ occurred $=2$

Total number of favorable outcomes $=2+3=5$

Probability of getting a number less than $3$

$=\frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$

$=\frac{5}{20}$

$=\frac{1}{4}$

Hence, probability of getting a number less than $3$ is $\frac{1}{4}$.