Class 10 Exam > Class 10 Questions > Cards marked wit h numbers 13, 14, 15,..........
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Cards marked wit h numbers 13, 14, 15,.......,60 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that number on the drawn card is
(i) divisible by 5.
(ii) a number which is a perfect square.
(i) divisible by 5.
(ii) a number which is a perfect square.
- a)5/24, 1/24
- b)5/24, 1/12
- c)1/12, 5/12
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Cards marked wit h numbers 13, 14, 15,.......,60 are placed in a box a...
To find the probability of drawing a card with a specific property, we need to determine the total number of cards in the box and the number of cards that satisfy the given condition.
Total number of cards in the box = 60 - 13 + 1 = 48
(i) Divisible by 5:
To find the number of cards divisible by 5, we need to determine the number of multiples of 5 between 13 and 60.
The first multiple of 5 greater than or equal to 13 is 15.
The last multiple of 5 less than or equal to 60 is 60.
Number of multiples of 5 = (60 - 15)/5 + 1 = 12
Therefore, the number of cards divisible by 5 = 12.
Probability of drawing a card divisible by 5 = (Number of cards divisible by 5) / (Total number of cards)
= 12/48
= 1/4
= 5/20
= 5/24
(ii) Perfect squares:
To find the number of perfect squares between 13 and 60, we need to determine the number of integers whose square lies between 13 and 60.
The smallest perfect square greater than or equal to 13 is 16.
The largest perfect square less than or equal to 60 is 49.
Number of perfect squares = (49 - 16)/1 + 1 = 34
Therefore, the number of cards that are perfect squares = 34.
Probability of drawing a card that is a perfect square = (Number of cards that are perfect squares) / (Total number of cards)
= 34/48
= 17/24
= 1/24 * 17/1
= 1/24
Hence, the correct answer is option B) 5/24 and 1/12.
Total number of cards in the box = 60 - 13 + 1 = 48
(i) Divisible by 5:
To find the number of cards divisible by 5, we need to determine the number of multiples of 5 between 13 and 60.
The first multiple of 5 greater than or equal to 13 is 15.
The last multiple of 5 less than or equal to 60 is 60.
Number of multiples of 5 = (60 - 15)/5 + 1 = 12
Therefore, the number of cards divisible by 5 = 12.
Probability of drawing a card divisible by 5 = (Number of cards divisible by 5) / (Total number of cards)
= 12/48
= 1/4
= 5/20
= 5/24
(ii) Perfect squares:
To find the number of perfect squares between 13 and 60, we need to determine the number of integers whose square lies between 13 and 60.
The smallest perfect square greater than or equal to 13 is 16.
The largest perfect square less than or equal to 60 is 49.
Number of perfect squares = (49 - 16)/1 + 1 = 34
Therefore, the number of cards that are perfect squares = 34.
Probability of drawing a card that is a perfect square = (Number of cards that are perfect squares) / (Total number of cards)
= 34/48
= 17/24
= 1/24 * 17/1
= 1/24
Hence, the correct answer is option B) 5/24 and 1/12.
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Community Answer
Cards marked wit h numbers 13, 14, 15,.......,60 are placed in a box a...
Outcomes are 13, 14, 15,.......,60.
Total number of possible outcomes = 60 - 12 = 48
(i) The numbers divisible by 5 are 15, 20, 25, 30, 35, 40, 45, 50, 55, 60.
Thus, the number of numbers divisible by 5 = 10
Required probability = 10/48 = 5/24
(ii) Perfect square numbers are 16, 25, 36, 49
Thus, the number of perfect square number = 4
Required probability = 4/48 = 1/12
Total number of possible outcomes = 60 - 12 = 48
(i) The numbers divisible by 5 are 15, 20, 25, 30, 35, 40, 45, 50, 55, 60.
Thus, the number of numbers divisible by 5 = 10
Required probability = 10/48 = 5/24
(ii) Perfect square numbers are 16, 25, 36, 49
Thus, the number of perfect square number = 4
Required probability = 4/48 = 1/12
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Cards marked wit h numbers 13, 14, 15,.......,60 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that number on the drawn card is(i) divisible by 5.(ii) a number which is a perfect square.a)5/24, 1/24b)5/24, 1/12c)1/12, 5/12d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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