Question

At a fete cards bearing numbers $1$ to $500$, one on each card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card bears a number which is a perfect square of an even number the player wins prize. What is the probability that the first player wins a prize$?$

Answer 1

Finding the probability that the first player wins a prize.

Let $\text{P}\left(\text{E}\right)$ be the probability that the first player wins a prize.

Total number of cards$=500$

$\therefore$Number of possible outcomes$=500$

Cards having number which is a perfect square of an even number from $1$ to $500$$=4,16,38,64,100,144,196,256,324,400,484$

$\therefore$Number of favourable outcomes$=11$

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{11}{500}$

Hence, probability that the first player wins a prize$=\frac{11}{500}$.