Say I collect 40 perfectly random integers between 1 and 400. What's the chance that any integer is repeated consecutively six times in such a random draw?
What I'm looking for is the chance of sequences like [372, 193, 42, 42, 42, 42, 42, 42, 274, 42, 7, ...]
, [372, 193, 42, 42, 42, 42, 42, 42, 274, 242, 7, ...]
, or [372, 193, 42, 42, 42, 42, 42, 42, 42, 42, 42, ...]
as they all fulfills what I'm looking for. As a counter example [372, 193, 42, 42, 42, 42, 42, 77, 274, 42, 7, ...]
does not satisfy my conditions because the six 42
's are not consecutively repeated.
The Birthday problem gives that it's an 87% chance that two of the 40 are the same number but I'm failing to go from that to calculating the chance of a certain integer consecutively repeating itself n number of times in the random collection.