Bizarre Bag of Balls

Discrete Mathematics Level 4

Two bags of balls each contain balls numbered $1, 2, \ldots , n$ . For how many values of $n$ such that $1 \leq n \leq 500$ , does there exist a $k$ such that the probability of getting a sum of $n+1$ when a ball is selected from each bag is equal to the probability that the sum is $\leq k$ when a ball is selected from each bag?

Details and assumptions

Since a ball is selected from each bag, there are 2 balls selected, and we are looking at the sum of these values.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 8 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.