A man repeatedly rolls a dice for infinity. What is the most number of sixes that would appear consecutively?

Question

It is assumed that the man never dies. He just sits and rolls a single dice over and over again for eternity. Is there a limit to how many times the number six will occur in a row? If so what is that limit?

Sorry I should have clarified.. it is a six sided dice.

Answer 1

No, there is not a limit.
He has a 1/6 chance of rolling a 6 on his next roll.
He has a (1/6)^2 chance of rolling two 6's
He has a (1/6)^3 chance of rolling three 6's

and so on

So, the probability that he will roll n 6's on his NEXT n rolls is (1/6)^n, therefore, however many 6's you want to say, yes, it is still possible for that to happen.

However, as n get larger and larger, the likelihood decreases to the point that we say it is a statistical impossibility -- that is to say, the chances of it happening become so slim that we don't EXPECT it to ever actually come to pass.

I hope this helps!

Answer 2

The more the die is rolled, the more equally distributed
the outcomes, 1,2,3,4,5,6 so that we may certainly say that
6 occurs approximately 1/6 of the time, 66 occurs 1/36 of the time, 66......6 (n sixes) occurs 1/6^n of the time and since the time is infinite, each one of these occurs infinitely often,
that is, (1/6^n)(infinity) = (infinity) for any choice of n. Therefore there is no limit to the number of sixes which can appear consecutively and also no limit to how often this will appear.

Answer 3

I'm not a mathematician, but I presume the maximum number of consectutive sixes is determined by the number of rolls. Since the number of rolls is infinite, so is the maximum number of sixes. The probability of rolling a number of sixes in a row would have to be divided by infinity, which would also yeild a number expressed as a part of infinity.

Answer 4

The danger which you will roll the quicker selection is: Roll danger a million a million/6 2 a million/6 * 5/6 3 a million/6 * (5/6)² and so on. The sum of those opportunities is given by way of the sum of the sequence. SUM = a + ar + ar² + ar^3 + --- = a/(a million - r) in this situation, a = a million/6 and r = 5/6 a/(a million - r) = (a million/6)/((a million/6) - 5/6)) = a million

Answer 5

Infinity

When you put infinity into the equation the only result is infinity.

No matter what the probability of him rolling the desired result he will come up with that combination an infinite number of times. And then you can always add one, that's infinity.

Answer 6

there's no limit but the chances are 1/6