What is the expected number of dice rolls until we get two 6’s in a row?

The answer IS 42

Step-by-step explanation:

First and foremost, we unquestionably have not recently hurled a 6, so is the desire required.

On the off chance that is the normal time of pausing on the off chance that we have quite recently hurled a 6.

f we have not recently hurled a 6, at that point with likelihood 56 we hurl a non-6 (cost: 1 hurl) and our normal extra holding up time is still . With likelihood 16 we hurl a 6 (cost: 1 hurl) and our normal extra holding up time is . Therefore

=1+5a/6+1b/6.

On the off chance that we have recently gotten a 6, at that point with likelihood 56 we get a non-6 hurl, and afterward our normal extra holding up time is . (With likelihood 16 the game is finished.)

Thus

=1+5a/6.

This gives us two direct conditions in two questions.

=1+5a/6+1b/6.

=1+5a/6.

If we solve for a, we get 42