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 $7$

Answer 1

Square numbers from 11 to 123$=16,25,36,49,64,81,100and121$

Total square number from 11 to 123$=8$

Total cards numbered from 11 to 123$=113$

(1) P(a square number)$=\frac{8}{113}$

Muliples of 7 from 11 to 123$=14,21,28,35,42,49,56,63,70,77,84,91,98,105,112,119$

Total multiples of 7 from 11 to 123$=16$

(2) P(a multiple of 7)$=\frac{16}{113}$