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What is the probability that the sum of any two different single digit natural numbers is a prime number ?
- a)5/27
- b)7/18
- c)1/3
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
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What is the probability that the sum of any two different single digit...
Total no. of two different single digit natural number = 9C2=36
The number of two different single digit natural no.s whose sum is a prime number ( 3,5 ,7 ,11,13 & 17) = 14
The number of two different single digit natural no.s whose sum is a prime number ( 3,5 ,7 ,11,13 & 17) = 14
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What is the probability that the sum of any two different single digit...
Solution:
Prime numbers between 1 to 9 are 2, 3, 5 and 7. Let's take all possible pairs of natural numbers whose sum is less than or equal to 9.
(1,2), (1,3), (1,4), (1,5), (1,6), (1,7), (1,8), (1,9)
(2,3), (2,4), (2,5), (2,6), (2,7), (2,8)
(3,4), (3,5), (3,6), (3,7)
(4,5), (4,6), (4,7)
(5,6), (5,7)
(6,7)
Out of these pairs, we can see that only 8 pairs have a sum that is a prime number.
(1,2), (1,4), (1,6), (2,3), (2,5), (3,4), (3,8), (4,3)
Therefore, the probability that the sum of any two different single digit natural numbers is a prime number is 8/36 or 7/18.
Answer: Option B. 7/18.
Prime numbers between 1 to 9 are 2, 3, 5 and 7. Let's take all possible pairs of natural numbers whose sum is less than or equal to 9.
(1,2), (1,3), (1,4), (1,5), (1,6), (1,7), (1,8), (1,9)
(2,3), (2,4), (2,5), (2,6), (2,7), (2,8)
(3,4), (3,5), (3,6), (3,7)
(4,5), (4,6), (4,7)
(5,6), (5,7)
(6,7)
Out of these pairs, we can see that only 8 pairs have a sum that is a prime number.
(1,2), (1,4), (1,6), (2,3), (2,5), (3,4), (3,8), (4,3)
Therefore, the probability that the sum of any two different single digit natural numbers is a prime number is 8/36 or 7/18.
Answer: Option B. 7/18.
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