Question

There are 100 cards in a bag on which numbers from 1 to 100 are written. A card is taken out from the bag at random. Find the probability that the number on the selected card (i) is divisible by 9 and is a perfect square, (ii) is a prime number greater than 80.

Answer 1

Number of possible outcomes = 100

(i) Let $E_1$ be the event of getting a number divisible by 9 and is a perfect square.

$\therefore$ Favourable outcomes = $\{9,36,81\}$

Number of favourable outcomes = 3

$\therefore P\left(E_1\right)=\frac{3}{100}$

(ii) Let $E_2$ be the event of getting a prime number greater than 80.

$\therefore$ Favourable outcomes = $\{83,89,97\}$

Number of favourable outcomes = 3

$\therefore P\left(E_2\right)=\frac{3}{100}$