What Are the Odds of an Event Occurring in Multiple Trials?

  • Thread starter Poop-Loops
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In summary, the conversation revolved around the calculation of the probability of getting a specific number (9) in a series of events (100 rolls). The formula for calculating the probability of at least one occurrence of the number was discussed, with one person providing a quick derivation while the other suggested summing a series of combinations. The conversation also touched upon the concept of combinations and their role in probability calculations.
  • #1
Poop-Loops
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This has bugged me for quite some time now, but I've always shrugged it off. I've taken a course in statistics and have dealt with them in one way or another for a few years, so I KNOW I've seen the answer to this, but I can't remember it and don't know where to look for it.

Well, I could crack open my statistics book, but I figure this would go faster.

Anyway, my question is as follows: The probability of something happening is 1/100. You do 100 iterations. What is the chance of it happening?

So for example you have a 100 sided die, and you roll it 100 times. What's the chance of getting a 9? I know I can't be 1. But it has to get closer as you get to infinity, right? I just can't think off the top of my head how that formulation would go.
 
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  • #2
What is the chance of getting exactly one nine or at least one nine?

I think at least one nine is 1-.99^100
 
  • #3
That makes sense. And yeah, I meant "at least", but "exactly" would be a good one to know, too. Thanks.
 
  • #4
I had to double check this one:

Exactly one nine is C(100,1)(.01^1)(.99^99)
then exactly two nines C(100,2)(.01^2)(.99^98)
and so on...
 
  • #5
Oh, duh, it's a combination.

Okay, but do you have a quick derivation for getting at least 1 number? It's not obvious to me how you would get that from seeing the formula, but I suspect it has something to do with combinations anyway.
 
  • #6
I didn't derive it. I just considered not no nines. So the probability of any result of 100 rolls (1) minus the probability of all the rolls being any number but nine (99^100). In this case nine, but it doesn't matter. The probability is the same for at least one of any single number 1-100.

I suppose you could sum the series of combinations. But that would be work I think.
 
  • #7
Ahh I gotcha. Thanks. :)
 

FAQ: What Are the Odds of an Event Occurring in Multiple Trials?

What is the definition of "chance of something happening"?

The chance of something happening is the likelihood or probability of a specific event occurring. It can range from 0% (impossible) to 100% (certain).

How is the chance of something happening calculated?

The chance of something happening is calculated by dividing the number of possible outcomes that result in the event by the total number of possible outcomes. This is known as the probability formula: P(Event) = Number of favorable outcomes / Total number of possible outcomes.

Can the chance of something happening be greater than 100%?

No, the chance of something happening cannot be greater than 100%. This would mean that the event is certain to occur, which goes against the definition of chance or probability.

How can we increase the chance of something happening?

The chance of something happening can be increased by increasing the number of favorable outcomes or decreasing the total number of possible outcomes. This can be achieved through various methods such as increasing sample size, changing the conditions of the experiment, or altering the variables.

Is the chance of something happening always accurate?

No, the chance of something happening is not always accurate. It is based on probability and there is always a level of uncertainty. It is important to note that a higher chance does not guarantee that the event will occur, and a lower chance does not mean that the event will not occur. It is simply a measure of likelihood.

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