Question

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 $0$

1. The probability that the sum of the numbers he gets is greater than 0 is 209/210.

### What is probability?

• Probability is the branch of mathematics concerned with numerical descriptions of the likelihood of an event occurring or of a proposition being true.
• The probability of an event is a number between 0 and 1, where 0 represents the event’s impossibility and 1 represents certainty.
• By dividing the favorable number of outcomes by the total number of possible outcomes, the probability of an event can be calculated.
To find 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 209/210.
Therefore, the probability that the sum of the numbers he gets is greater than 0 is 209/210.