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(a) A bag contains $40$ marbles out of which some are white and others are black. If the probability of drawing a black marble is $\frac{3}{5}$, then find the number of white marbles.
OR
(b) In a pre-primary class, a teacher put cards numbered $20$ to $59$ in a bowl. A student picked up a card at random and read the number. Find the probability that the number read was (i) a prime number (ii) a perfect square.
OR
(b) In a pre-primary class, a teacher put cards numbered $20$ to $59$ in a bowl. A student picked up a card at random and read the number. Find the probability that the number read was (i) a prime number (ii) a perfect square.
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Solution: (a) Let the number of black marbles be $n$.
$P(\text{drawing a black marble}) = \frac{n}{40}$
$\therefore \frac{3}{5} = \frac{n}{40} \Rightarrow n = 24$
Hence, number of white marbles $= 16$
OR
(b) Total number of cards $= 40$
(i) $P(\text{a prime number}) = \frac{9}{40}$
(ii) $P(\text{no. is perfect square}) = \frac{3}{40}$
$P(\text{drawing a black marble}) = \frac{n}{40}$
$\therefore \frac{3}{5} = \frac{n}{40} \Rightarrow n = 24$
Hence, number of white marbles $= 16$
OR
(b) Total number of cards $= 40$
(i) $P(\text{a prime number}) = \frac{9}{40}$
(ii) $P(\text{no. is perfect square}) = \frac{3}{40}$