what is the probability that sum of any two different single digit natural numbers is a prime number
Answers
Answer:
Step-by-step explanation:
set of single digit natural numbers includes N : {1,2,3,4,5,6,7,8,9}
...
now, the maximum sum that you can get is 9+9=18 ( since it's not mentioned in the qurstion , so we can use same digit twice ).
So,
primes numbers that we can have are, 2 , 3 , 5 , 7 , 11 , 13 , 17
Now solve for different prime numbers!
...
1+1
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
[ Since there is no condition on picking up the numbers, hence 1+2 and 2+1 is same ]
So,
These are the only 15 cases where we'll have a prime number...
Total number of ways of adding two single digit natural numbers are = 9 + 8 + 7 + 6 + ........+ 1 = 45
...
Hence the probability is 15/45 = 1/3
...
*** Now here is a thing, if you are looking for two different natural numbers,
Then;
The probability will be 14/36 = 7/18
7/18 is the correct answer