an integer is chosen between 0 and 100 what is the probability that it is :

(1) divisible by 9

(2) a perfect square number

The list of numbers between 0 and 100 are : 1, 2, 3, 4, 5,...........99
total possible outcomes = 99
numbers which are divisible by 9 are : 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99
no. of favorable outcomes = 11

probabilty(no. is divisible by 9) = number of favorable outcomesno. of possible outcomesprobabilty(no. is divisible by 9)  = 1199 = 19 Perfect square numbers between 0 and 100 are : {1,4,9,16,25,36,49,64,81}number of perfect squares = 9no. of favorable outcomes = 9probabilty( the number is perfect square) = number of favorable outcomesno. of possible outcomes=999=111
 

  • 12

here the first term or the first number which will be divisible by 9 between 0 and 100 will be

a = 9

and the last number will

an or l = 99

d = 9

so n= ?

an = a + ( n-1) * d

99 = 9 + ( n - 1 ) 9

99 = 9 + 9n - 9

99 = 9n

n = 99 / 9

n = 11

  • 6
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