# Probability Problem

1. Oct 8, 2005

### chocok

A box contains tickets marked 1,2,......,n. Two tickets are drawn at random from the box. What is the probability the second number drawn is bigger than the first number drawn?
The answer shown is (1-1/n)/2. But... how?

2. Oct 8, 2005

### Tide

What happens when n = 2?

3. Oct 8, 2005

### HallsofIvy

Tide's point is that the "answer shown" is WRONG. It shouldn't take a whole lot of thought to see that the probability that "the second number drawn is bigger than the first number" is exactly the same as the probability that "the first number drawn is bigger than the second number.

4. Oct 8, 2005

### Danger

Just out of curiosity, where did you get that formula?

5. Oct 8, 2005

### chocok

Sorry to all, forgot to mention that this is "sampling with replacement". So, by using HallsofIvy's hint, I know how to derive it now. Thanks! And just curious, the answer for without replacement is 1/2?

HallsofIvy, can you give more explanation on "the second number drawn is bigger than the first number" is exactly the same as the probability that "the first number drawn is bigger than the second number"? they sound more like compliments to me with one higher and one lower probability....

Last edited: Oct 8, 2005