Question

An integer is chosen at random from $1$ to $50$. Find the probability that a number is a prime number.

Answer 1

Find the probability that a number is a prime number:

Given that we have to choose a number from $1$ to $50$.

Then the total number of outcomes $=50$

According to the question,

Numbers that are prime from $1$ to $50$ are $2,3,5,7,11,13,17,19,23,29,31,37,41,43,47$

Then the total number of favorable outcomes $=15$

We know that $\mathrm{Probability}=\frac{\mathrm{number}\mathrm{of}\mathrm{favorable}\mathrm{outcomes}}{\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}$

$$\begin{gathered} =\frac{15}{50} \\ =\frac{3}{10} \end{gathered}$$

Therefore the required probability is $\frac{3}{10}$.