Question 537280
Let P stand for probability
( P that sum of digits exceeds 5 ) + ( P that sum is 5 or less ) = 1
The probabilities of everything that can possibly happen
must add up to one, therefore:
( P that sum of digits exceeds 5 ) = 1 - ( P that sum is 5 or less )
The 2 digit numbers that are 5 or less are
10,11,12,13,14
20,21,22,23
30,31,32
40,41
50
There are 15 of these numbers
The sum of digits of all the other 2 digit numbers exceed 5
The tens digit can be 1 - 9, or 9 possible
The units digit can be 0 - 9 or 10 possible
Total possible numbers = {{{ 9*10 = 90 }}}
{{{ 15/90 }}} = P that sum is 5 or less
{{{ 1 - 15/90 = 90/90 - 15/90 }}}
{{{ 1 - 15/90 = 75/90 }}}
{{{ 75/90 = 5/6 }}}
P that sum of digits exceeds 5 = 5/6