You randomly pick two numbers from 1 to 9. if you could pick the same number twice and the first of the two numbers are in less than five in the probability that the sum of the two numbers is less than five is

Alright, so the number is less than 5, we pick it twice, and the sum (2*number) is less than 5, we have 2 options - 2 or 1. 3 or more doesn't work because 3*2=6. The probability of choosing 2 is 1/9, and choosing 2 again is 1/9. Since they don't have anything to do with each other, we multiply 1/9 by 1/9 to get 1/81 as the chance of choosing 2 twice. Since we can have 1 twice too, we add 1/81 to 1/81 to get 2/81