# Probability of a certain sequence when rolling dices

• Sep 4th 2007, 02:00 AM
Maxim
Probability of a certain sequence when rolling dices
I roll a dice 50 times. What is the probability that there is a(t least one) sequence of (at least) 5 consecutive sixes in the result?

For example, suppose somewhere in my sequence of 50 dice results, there is:
...46166666332...
Then it's a "hit" cause it contains 5 consecutive sixes.

I can't decide how to approach this: as a counting / combination problem, or as a probability problem. In either case I can't figure out how to avoid counting combinations or possibilities twice... :confused:
• Sep 4th 2007, 03:27 AM
JakeD
Quote:

Originally Posted by Maxim
I roll a dice 50 times. What is the probability that there is a(t least one) sequence of (at least) 5 consecutive sixes in the result?

For example, suppose somewhere in my sequence of 50 dice results, there is:
...46166666332...
Then it's a "hit" cause it contains 5 consecutive sixes.

I can't decide how to approach this: as a counting / combination problem, or as a probability problem. In either case I can't figure out how to avoid counting combinations or possibilities twice... :confused:

This is the same kind of problem as in this thread.