Question

In a lottery of $50$ tickets numbered $1$to $50$ one ticket is drawn. Find the probability that the drawn ticket bears a prime number.

Answer 1

Step 1: Use formula of probability

$P\left(A\right)=\frac{\text{number of outcome favourable to A}}{\text{total number of possible outcome}}$

or

$P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}$

where,

• $P\left(A\right)$is probability of an event$\text{'}A\text{'}$
• $n\left(A\right)$is the favorable outcome of the event $\text{'}A\text{'}$

$n\left(S\right)$is total number of possible outcome in a sample space

Step 2: The probability of getting a prime number on ticket

Let, A be the event of “getting a prime number on ticket ”

Then, Total number of tickets is $50$ .

$S$ is a sample space of all the possible outcomes which is $50$tickets.

Thus, total number of possible outcome in a sample space is $n\left(S\right)=50$

Number of prime numbers are

$2,3,5,7,11,13,17,19,23,29,31,37,41,43\text{and 47}$.

Thus, the favorable outcome of the event $\text{'}A\text{'}$ is $n\left(A\right)=15$

The probability of getting a prime number on ticket $P\left(A\right)$is,

$P\left(A\right)=\frac{\text{number of tickets with prime number}}{\text{total number of tickets}}=\frac{n\left(A\right)}{n\left(S\right)}$

Substitute the values on the formula,

$P\left(A\right)=\frac{15}{50}=\frac{3}{10}$

Hence, the probability of getting a prime number on ticket is $\frac{3}{10}$.