Bob plays a game where, for some number n , he chooses a random integer between 0 and n-1 , inclusive. If Bob plays this game for each of the first four prime numbers, what is the probability that the sum of the numbers he gets is greater than 0?
The first four prime numbers are 2,3,5,7
So for the first game, he chooses either 0 or 1
For the second one, he chooses 0,1, or 2
For the third, he chooses 0,1,2,3 or 4
For the fourth, he chooses 0,1,2,3,4,5, or 6
There are a total of \(2*3*5*7=210\)choices
There is only one case where the sum is zero
So there are 209 cases where the sum is greater than zero
The probability that the sum is greater than zero is thus \(209/210\).