Question

$20$ cards numbered $1,2,3,...,20$ are put in a box and mixed thoroughly. Shashi draws a card from the box. Find the probability that the number on the card is even.

Answer 1

Finding the probability that the number on the card is even.

Let $\text{P}\left(\text{E}\right)$ be the probability that the number on the card is even.

Total number of cards$=20$

$\therefore$Number of possible outcomes$=20$

Outcomes with even numbers$=2,4,6,8,10,12,14,16,18$ and $20$

$\therefore$Number of favourable outcomes$=10$

We know that $\text{P}\left(\text{E}\right)\text{=}\frac{\text{Number of favourable outcomes}}{\text{Number of possible outcomes}}$

So, $\text{P}\left(\text{E}\right)$$=\frac{10}{20}$

$=\frac{\mathbf{1}}{\mathbf{2}}$

Hence, probability that the number on the card is even$=\frac{\mathbf{1}}{\mathbf{2}}$