Question

Problem 28. A fair six-sided die is rolled repeatedly and the rolls are recorded. When two consecutive rolls are identical, the process is ended. Let S denote the sum of all the rolls made. Is S more likely to be even, odd or just as likely even as odd?

Answer 1

answer:

Reasonable six sided bite the dust is moved over and again and rolls are recorded.

The procedure is finished when two sequential rolls are indistinguishable.

Lets say there are n moves before getting 2 continuous rolls.

In this way,

Likelihood of getting aggregate is an Odd number of these n rolls = Probability of getting whole is a much number of these n rolls.

It is on the grounds that these rolls are free of one another.

Presently we moved it two times progressively and get indistinguishable rolls that implies the entirety of these two rolls will dependably be Even (1,1) , (2,2), (3,3) , (4,4), (5,5) ,(6,6) all are even in total.

In this way, when we include these two comes in the whole of n numbers it will dependably be a similar sort (Odd or even) just like the total os n numbers.

Like if whole of n number was and still, at the end of the day total of (n+2) number will likewise be even.

on the off chance that aggregate of n number was odd at that point entirety of (n+2) number will likewise be odd.

Along these lines, that implies Probability of getting whole of all rolls even is same as getting total of all rolls odd.

so S is similarly as likely even as odd.