Question

A box contains cards numbered from 10 to 120. A card is drawn at random from the box. Find the probability that the number of the card is
(i) A perfect square number
(ii) A multiple of 9.

Answer 1

total no. of events = 111
1) the no. between 10 and 120 which are perfect square are
                        16 , 25 , 36 , 49 , 64 , 81 , 100
probability of getting a perfect square = 7/111

2) the no. which are mutiple of 9 between 10 and 120 are 
                         18 , 27 , 36 , 45 , 54 , 63 , 72 , 81 , 90 , 99 , 108 , 117
probability of getting a multiple of 9 = 12/111                       

Answer 2

SAMPLE SPACE(s):
S={10,11,12.........................120}
n(s)=111

LET A be the event that the number of the card is a perfect square.

A={16,25,36,49,64,81,100,}
n(A)=7
P(A)= n(A)/n(S)
P(A)=7/111

Let B be the event that the number of the card is a multiple of 9.

B={18,27,36,45,54,63,72,81,90,99,108,117}
n(B)=12

P(B)=n(B)/n(S)
P(B)=12/111

THEREFORE,
1)THE PROBABILITY THAT THE CARD IS A PERFECT SQUARE IS 7/111
2)THE PROBABILITY THAT THE CARD IS A MULTIPLE OF 9 IS 12/111

hope this helps