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What is the probability that the sum of ...

What is the probability that the sum of any two different single digit natural numbers is a prime number?

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We know single digit natural number are from `1` to `9`.
Now, the maximum sum that we can get is `9+8=17` as we have to use different numbers.
Now, possible two digits having a sum equal to prime number are,
`(1+2),(1+4),(2+3),(1+6),(2+5),(3+4),(2+9),(3+8),(4+7),(5+6),`
`(4+9),(5+8),(6+7),(8+9)`.
So, there are `14` possible values.
Now, number of ways selecting these `2` digits from `9` digits is `C(9,2)`.
`:.` the required probability ` = 14/(C(9,2)) = 14/36 = 7/18`
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