Probability of two things happening at the same time

In summary, the probability of two things happening at the exact same time, such as two arrows hitting a target simultaneously, is considered to be one in infinity. However, the probability of three things happening at the same time is still considered to be zero. This is because the probability of selecting a specific point or time from a continuous distribution is always zero, and you can only talk about the probability of a value in an interval. Therefore, the probability of multiple events occurring at the exact same time is always considered to be zero.
  • #1
Dr Chaos
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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?
 
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  • #2
You are making things needlessly complicated. Both probabilities are 0.
 
  • #3
But surely it is possible for two arrows to hit a target at once?
 
  • #5
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
mathman said:
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?
 
  • #7
Dr Chaos said:
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.
 
  • #8
CRGreathouse said:
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.
 
  • #9
Dr Chaos said:
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.
 

FAQ: Probability of two things happening at the same time

What does it mean for two events to occur at the same time?

When we say two events occur at the same time, it means that they happen simultaneously or at the exact same moment.

How do you calculate the probability of two events happening at the same time?

The probability of two events happening at the same time is calculated by multiplying the individual probabilities of each event. This is also known as the "and" rule in probability.

Can the probability of two events happening at the same time be greater than 1?

No, the probability of two events happening at the same time cannot be greater than 1. This is because the probability of an event occurring ranges from 0 to 1, where 0 represents impossibility and 1 represents certainty.

Is the probability of two events happening at the same time affected by the probability of each event?

Yes, the probability of two events happening at the same time is affected by the probability of each event. The higher the probability of each event, the higher the probability of both events occurring at the same time.

How can the probability of two events happening at the same time be used in real life?

The probability of two events happening at the same time can be used in various real-life situations, such as predicting the likelihood of two weather events occurring simultaneously or calculating the chances of winning multiple prizes in a lottery.

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