There are 100 cards in a bag on which numbers from 1 to 100 are written. A card is taken out from the bag at random. Find the probability that the number on the selected card is divisible by 9 and is a perfect square.

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3100

9100

6100

81100

answer is A.

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Detailed Solution

Given, there are 100 cards in a bag on which numbers from 1 to 100 are written. A card is taken out from the bag at random.
The probability of an event to be occurred is the division of the number of favourable outcomes by the total number of outcomes that is,

Probability of an event = Number of favourable outcomes Total number of outcomes

Find the number of favourable outcomes.
Total number of cards in the bag is 100, that is, the total number of outcomes is 100.
The numbers which are divisible by 9 and are also perfect squares are

32, 62

, and

92

that is, 9, 36 and 81 respectively.
So, the number of perfect squares which are divisible by 9 is 3 which is the number of favourable outcomes.
Find the required probability by dividing the number of favourable outcomes by the total number of outcomes that is, 3 and 100 respectively.