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There is a stack of 150 cards which contains cards numbered from 1 to 150. A card is drawn randomly from this stack. What is the probability that the card drawn is either a square or a cube of a natural number, but not both?
- a)11/150
- b)1/10
- c)13/150
- d)7/75
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
There is a stack of 150 cards which contains cards numbered from 1 to ...
Given: A stack of 150 cards containing cards numbered from 1 to 150.
To find: Probability of drawing a card which is either a square or a cube of a natural number, but not both.
Solution:
- Total number of cards = 150
- Number of cards which are perfect squares = 12 (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144)
- Number of cards which are perfect cubes = 5 (1, 8, 27, 64, 125)
- Number of cards which are both perfect squares and cubes = 2 (1, 64)
- Number of cards which are either perfect squares or perfect cubes but not both = 12 + 5 - 2 = 15
Therefore, the probability of drawing a card which is either a square or a cube of a natural number, but not both = 15/150 = 1/10.
Hence, option (b) is the correct answer.
To find: Probability of drawing a card which is either a square or a cube of a natural number, but not both.
Solution:
- Total number of cards = 150
- Number of cards which are perfect squares = 12 (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144)
- Number of cards which are perfect cubes = 5 (1, 8, 27, 64, 125)
- Number of cards which are both perfect squares and cubes = 2 (1, 64)
- Number of cards which are either perfect squares or perfect cubes but not both = 12 + 5 - 2 = 15
Therefore, the probability of drawing a card which is either a square or a cube of a natural number, but not both = 15/150 = 1/10.
Hence, option (b) is the correct answer.
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Community Answer
There is a stack of 150 cards which contains cards numbered from 1 to ...
Total favourable possible nos. = 4, 8, 9, 27, 16, 25, 125, 36, 49, 81, 100, 121, 144
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There is a stack of 150 cards which contains cards numbered from 1 to 150. A card is drawn randomly from this stack. What is the probability that the card drawn is either a square or a cube of a natural number, but not both?a)11/150b)1/10c)13/150d)7/75Correct answer is option 'C'. Can you explain this answer?
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