To Alan: Your were asked this simple question some 8 hours ago:
What are the odds of getting the same number thrice when throwing one dice (1-6) three times?
And you gave this answer:
Alan
The probability that the second throw is the same as the first is 1/6. The probability that the third throw is the same is 1/6. Therefore the overall probability that they are all the same is (1/6)*(1/6) = 1/36.
In terms of odds this is probably expressed as 35 to 1 against, since 35 in every 36 tries they won't be the same, and once in every 36 tries they will be the same.
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Why is it different from this mathematicain's response to the same question:
For three rolls, there is a 1/6 probability of rolling a six on the first
roll. There is a 5/6 probability that the first roll is not a 6. In that
case, we need to see if the second roll is a 6. The probability of the second
roll being a 6 is 1/6, giving us a probability of 11/36. There is a 25/36
probability that neither of the first two rolls was a 6. In that case, we
need to see if the third roll is a 6. The probability of the third roll being
a 6 is 1/6, giving us a probability of 1/6 + (5/6)*(1/6) + (25/36)*(1/6) =
91/216. Again, this is less than 3/6.
+33661 Are you sure it was the same question?
Firstly, the other reply seems to refer only to the number 6, whereas the question that I answered required all the throws to be the same (could be all 1s, all 2s ...etc. not just all 6s).
Secondly, the other reply seems to be calculating the probability that the first roll is a 6 or the second roll is a 6 or the third roll is a 6, whereas the question I answered required the first throw and the second throw and the third throw to be the same.
Definitely not answering the same question!
