# Probability of two things happening at the same time

1. Jul 14, 2010

### Dr Chaos

As there are an infinite number of time frames, does that mean that the probability of two things happening at the exact same time is one in infinity? (For example, two arrows hitting a target simultaneously).

If so, what is the probability of three things happening at the same time? Less than one in infinity?

2. Jul 14, 2010

### mathman

You are making things needlessly complicated. Both probabilities are 0.

3. Jul 14, 2010

### Dr Chaos

But surely it is possible for two arrows to hit a target at once?

4. Jul 14, 2010

### CRGreathouse

5. Jul 15, 2010

### mathman

Things that are possible may have zero probability. For example, everyone has a weight, but the probability that your weight is exactly a given value is zero. The point being if you are selecting from a continuous distribution, any given choice has a zero probability - you can only meaningfully talk about probability of a value in some interval.

6. Jul 15, 2010

### Dr Chaos

So does that mean that the probability of two arrows hitting a target at once is the same as with three?

7. Jul 15, 2010

### CRGreathouse

A target has nonzero size, so no. But two arrows and three arrows would (under that model, at least) have probability 0 to hit the same point.

8. Jul 15, 2010

### Dr Chaos

They don't have to hit the same point on the target - they just have to hit it at the exact same time.

9. Jul 15, 2010

### CRGreathouse

Then yes, probability 0.