Anonymous

If you, for example, take two dice and roll them both at the same time, what is the chance that at least one will be a six?

I'm wondering, because if you just add 1/6th+1/6th, you get 1/3rd. Which is fine and dandy, but what if you roll those two dice 6 times? You get 1. Yet you could at the same time not once roll a six even if you rolled 50 times. I understand the probability would go up, but never be 1. I'm looking more for the formula, rather than just someone telling me what I'm doing wrong.

Update:

Thank you; :D.

I knew 1/6th * 1/6th, but I did not know about the complements, thank you; that helped a lot.

So..

49/50 * 49/50 = 2401/2500ths. .. or 99/2500ths? Roughly 1/25th?

Relevance

If you only want at least one 6, you are really looking for the complement of the chance that you roll twice and don't get a 6.

There is a 5/6 chance that you don't get a 6 on any one roll. So with two rolls, multiply (this is a basic counting/probability principle) the probabilities of NOT getting a 6 together:

5/6 * 5/6 = 25/36

Again, this is the chance that you roll twice and get two non-6s. So the rest of the time, 11/36 times, you will get at least one 6.

You should only add the probabilities if you want to know the chances of, say, rolling a 6 or a 5 on one roll. Whenever you are dealing with multiple, independent events, you need to multiply probabilities together to find the probability of both things happening. For example, the chances of both dice landing on 6 are 1/6 * 1/6 = 1/36.

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• For these sort of questions it is easier if you put the question the other way around : 'roll two dice, what will the chance of neither having a six'.

For one die the chance is 5/6 of not getting a six. Therefore for two dice the chance is 5/6 x 5/6 = 25/36 of not getting a six. Therefore the chance of getting at least one six from 2 dice is 1 - 25/36 = 11/36.

Then extending this to the chance of no sixes from two throws of two dice - this would be 25/36 x 25/36. Therefore the chance of getting at least one six on two throws is 1 - 25/36 x 25/36 - approx 0.5

Rolling the two dice six times:

prob(6) = 1 - (25/36)^6 - approx 0.88

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• Anonymous
3 years ago

Chance Of Something Happening

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