Question

The number 71 is written as a sum of three natural numbers
71=a+b+c
(the triple (a,b,c) is ordered; e.g., the decompositions 71=1+1+69 and 71=1+69+1 are different.
Also, assume that all the decompositions have equal probability.)
What is the probability that there exists a triangle with sides a, b, and c?

Answer 1

Answer:

The first 50 natural numbers are 1,2,3,...,50

We know that, the sum of first n natural numbers is 2n(n+1)

Therefore, sum of first 50 natural numbers is 250(51)=25(51)=1275

Hence, the average of first 50 natural numbers is 501275=25.5