Probability of two things happening at the same time

[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?

[mathman]

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

[Dr Chaos]

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

[CRGreathouse]

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

http://en.wikipedia.org/wiki/Almost_surely

[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.

[Dr Chaos]

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.

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

[CRGreathouse]

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

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.

[Dr Chaos]

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.

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

[CRGreathouse]

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

Then yes, probability 0.