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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.
- a)9/100
- b)1/25
- c)7/100
- d)3/100
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
There are 100 cards in a bag on which numbers from 1 to 100 are writte...
Total num ber of possible outcomes = 100
Numbers from 1 to 100 which are divisible by 9 and perfect square are 9, 36 and 81.
Number of favourable outcomes = 3
∴ Required probability = 3/100
Numbers from 1 to 100 which are divisible by 9 and perfect square are 9, 36 and 81.
Number of favourable outcomes = 3
∴ Required probability = 3/100
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There are 100 cards in a bag on which numbers from 1 to 100 are writte...
Problem:
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.
Solution:
To find the probability that the number on the selected card is divisible by 9 and is a perfect square, we need to determine the number of cards that satisfy both conditions and divide it by the total number of cards.
Step 1: Determine the number of cards that are divisible by 9:
To find the number of cards that are divisible by 9, we need to determine the number of multiples of 9 between 1 and 100.
The first multiple of 9 between 1 and 100 is 9 itself. The last multiple of 9 between 1 and 100 is 99. So, the number of cards that are divisible by 9 is 99 / 9 = 11.
Step 2: Determine the number of perfect square cards:
To find the number of perfect square cards, we need to determine the number of perfect squares between 1 and 100.
The perfect squares between 1 and 100 are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. So, the number of perfect square cards is 10.
Step 3: Determine the number of cards that satisfy both conditions:
To find the number of cards that are divisible by 9 and are perfect squares, we need to find the common elements between the two sets.
The common elements between the multiples of 9 and perfect squares are 9, 36, and 81. So, the number of cards that satisfy both conditions is 3.
Step 4: Calculate the probability:
The probability is given by the number of favorable outcomes divided by the total number of outcomes.
Number of favorable outcomes = 3
Total number of outcomes = 100
Probability = 3 / 100 = 0.03 = 3/100
Therefore, the correct answer is option 'D', 3/100.
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.
Solution:
To find the probability that the number on the selected card is divisible by 9 and is a perfect square, we need to determine the number of cards that satisfy both conditions and divide it by the total number of cards.
Step 1: Determine the number of cards that are divisible by 9:
To find the number of cards that are divisible by 9, we need to determine the number of multiples of 9 between 1 and 100.
The first multiple of 9 between 1 and 100 is 9 itself. The last multiple of 9 between 1 and 100 is 99. So, the number of cards that are divisible by 9 is 99 / 9 = 11.
Step 2: Determine the number of perfect square cards:
To find the number of perfect square cards, we need to determine the number of perfect squares between 1 and 100.
The perfect squares between 1 and 100 are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. So, the number of perfect square cards is 10.
Step 3: Determine the number of cards that satisfy both conditions:
To find the number of cards that are divisible by 9 and are perfect squares, we need to find the common elements between the two sets.
The common elements between the multiples of 9 and perfect squares are 9, 36, and 81. So, the number of cards that satisfy both conditions is 3.
Step 4: Calculate the probability:
The probability is given by the number of favorable outcomes divided by the total number of outcomes.
Number of favorable outcomes = 3
Total number of outcomes = 100
Probability = 3 / 100 = 0.03 = 3/100
Therefore, the correct answer is option 'D', 3/100.
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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.a)9/100b)1/25c)7/100d)3/100Correct answer is option 'D'. Can you explain this answer?
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