Question

$50$ tickets numbered from $1$ to $50$ are put into an urn and mixed thoroughly. A ticket is drawn from the urn. Find the probability that the drawn ticket bears a prime number.

Answer 1

Step 1: Find the number of possible and favorable outcomes

Let E be an event of getting a prime number in the event of drawing a lottery ticket from the tickets numbered from $1$ to $50$ .

Prime numbers upto$50=\{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47\}$

Number of favorable outcomes$=15$

Total number of possible outcomes $=50$

Step 2: Use the formula for probability:

$P\left(E\right)=\frac{(No.offavorableoutcomes)}{(Totalno.ofpossibleoutcomes)}$

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

Final answer:

The probability that the drawn ticket bears a prime number is $\frac{3}{10}$.