Question

A fair dice is rolled. Each time the value is noted and running sum is maintained. What is the expected number of runs needed so that the sum is even ?
Can anyone tell how to solve this problem ?

Answer 1

Let's look at this, here are the roll possibilities for the two dice
E + E = E,
E + O = O,
O+O = E

Now lets look at some running totals for the two dice together

E - Even (if the first roll total is even then you're done, let's look if it wasn't)
O, O - Even
O,E,O - Even
O,E,E,E,E....... never

Now, if I misunderstood because you wrote dice and meant die.. you could skip to the second part there looking at the total being even or odd...

Not sure if that's what you're looking for but it's what I have off the top of my head ;)