[KAV] How many times number appeared immediately after the previous appearance?

[VLS]

Kav wrote:

Take any number. Let's say number 1.
In 1000 appearances of this number,
how many times the number appeared immediately after the previous appearance (in the next spin)
how many times it appeared after exactly 2 spins
how many times after exactly 3 spins
etc.
etc.
how many times it appeared after exactly 100 spins
etc.
etc.

Is there anyone who can run such a simulation and tell us the results?
Or can someone calculate these numbers using probability theory?

thanks

Bayes answered:

If I understand you correctly, you need to use the geometric distribution. The probability that the first success will occur on the x^th trial is:

p(x) = p(1 - p)^x-1

So for a single number, p = 1/37 and 1 - p = 36/37

The probability that the number will hit on the first spin is p(1) = 1/37 Ãâ€" (36/37)⁰ = 1/37

The probability that the number will hit on the second spin is p(2) = 1/37 Ãâ€" (36/37)¹

The probability that the number will hit on the third spin is p(3) = 1/37 Ãâ€" (36/37)²

The probability that the number will hit on the fourth spin is p(4) = 1/37 Ãâ€" (36/37)³

See the pattern?

You can easily set this up in a spreadsheet.