Question

A box contains cards numbered $11$ to $123$. A card is drawn at random from the box. Find the probability that the number on the drawn card is
(i) A square number
(ii) A multiple of $7$

• A. $\frac{48}{113},\frac{16}{113}$
• B. $\frac{8}{113},\frac{16}{113}$
• C. $\frac{8}{113},\frac{16}{143}$
• D. $\frac{8}{113},\frac{16}{155}$

Answer 1

The correct option is B $\frac{8}{113},\frac{16}{113}$

Cards in the number from $1$ to $123$

The perfect squares are : $16,25,36,49,64,81,100,121$

Total numbers $=113$

Total perfect squares $=8$

$\Rightarrow P$( A square number) $+\frac{8}{113}$

Multiple of $7$ are $:14,21,28,35,............119$

Total multiples of $7=16$

$\Rightarrow P$(A multiple of $7$)$=\frac{16}{113}$