Fixed symbol

Interesting question!
let's say we have slot 5x3 symbols (5 reels with 3 symbols per reel). On the first spin we fixed position of one symbol "A". There are may be several of them on diferent positions. On the next spin we get another specific symbol "B" on the same (fixed) position.
Probability of appearing of each symbol is the same on each of 15 positions. P(A) and P(B)
What is the probability of whis event (matching symbols during two spins)?

Quote: Myshell

Interesting question!
let's say we have slot 5x3 symbols (5 reels with 3 symbols per reel). On the first spin we fixed position of one symbol "A". There are may be several of them on diferent positions. On the next spin we get another specific symbol "B" on the same (fixed) position.
Probability of appearing of each symbol is the same on each of 15 positions. P(A) and P(B)
What is the probability of whis event (matching symbols during two spins)?
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This question is not clear to me. How many positions are shown on each reel (is it 3 positions per reel with 5 reels?) Can a position be blank or is it limited to being one of the three symbols?

If the slot shows 15 positions, 3 positions on each of 5 reels, and each position is filled randomly with one of three symbols:

Given a known symbol on a specific position, the probability of any specific pattern on the other 14 positions is 1 in 3¹⁴ or a probability of about 0.000000209075.

Thank you for your interest!
Yes, the slot shows 15 positions. It is 3 positions per reel with 5 reels.Each position is filled randomly with one of the limited set of symbols.
The probability of appearing symbol A on each position is P(A)
The probability of appearing symbol B on each position is P(B)
On the first spin, any number of symbol 'A' can fall out on diferent places(from 1 to 15). What is the probability, on the second spin, the appearance of the symbol 'B' on the same places where the symbol A appeared on the first spin?

Quote: Myshell

Thank you for your interest!
Yes, the slot shows 15 positions. It is 3 positions per reel with 5 reels.Each position is filled randomly with one of the limited set of symbols.
The probability of appearing symbol A on each position is P(A)
The probability of appearing symbol B on each position is P(B)
On the first spin, any number of symbol 'A' can fall out on diferent places(from 1 to 15). What is the probability, on the second spin, the appearance of the symbol 'B' on the same places where the symbol A appeared on the first spin?
link to original post

So, you want the probability that on the second spin the B symbol will exactly duplicate the pattern of the A symbol on first spin? I'll take a stab at it:

Let your P(A) = a
P(B) = b

Let p(n) be the probability that the A symbol appears n times on the first spin, and that the second spin results in a pattern of B symbols that exactly match the A symbol pattern of the first spin.

Then p(n) = aⁿ * (1-a)^(15-n) * c(15,n) * bⁿ * (1-b)^(15-n)

where c(m,n) is the combination function.

and, the total probability of this event occurring is: Σ p(n) where the summation is over n = 0 to 15.

I would appreciate it if other forum members review this, since I'm human and seem to make more than my share of mistakes.

Yes, its seems like a right way.
But that will be in case if 'A' symbol fall out n times. And 'B' symbol can fall out less than n times?
For example 'B' appear on the apropriate place on one out of n places.
or 'B' appear on the apropriate place two out of n places.

Quote: Myshell

Yes, its seems like a right way.
But that will be in case if 'A' symbol fall out n times. And 'B' symbol can fall out less than n times?
For example 'B' appear on the apropriate place on one out of n places.
or 'B' appear on the apropriate place two out of n places.
link to original post

Well, I'm asking for review and I may be wrong. But let me explain the algebraic formula for p(n), remembering that a= probability of any specific spot "rolling" an A symbol and that b = probability of any specific spot "rolling" a B symbol.

The probability that the A symbol appear n times on the first spin is:


Multiplying the first two terms by the combination formula accounts for the fact that when A appears n times there are many combinations of specific places (out of the 15 possible spaces) that n symbols can occur.

To have exactly n B symbols occur on the subsequent spin and occur in whatever the pattern was of the n A symbols in the first spin has a probability


Here, for each spot where an A symbol occurred in the first spin, the spot must roll a B symbol and the probability of that (for each specific spot) = b; and for n spots the probability is bⁿ.

For each spot where an A symbol did not occur on the first spin, the chance that a B symbol will not occur is (1-b) -and the probability of that occurring in all (15-n) such spots is (1-b)^(15-n). And I think that's all of the terms we need! No combination function is part of this term because there is only one specific combination(or pattern) of n spots that will qualify as a match with the first spin.

Let's give this 12-24 hours and let some of the super-brainiacs on this site weigh in with their comments.

Quote: gordonm888

Quote: Myshell

Thank you for your interest!
Yes, the slot shows 15 positions. It is 3 positions per reel with 5 reels.Each position is filled randomly with one of the limited set of symbols.
The probability of appearing symbol A on each position is P(A)
The probability of appearing symbol B on each position is P(B)
On the first spin, any number of symbol 'A' can fall out on diferent places(from 1 to 15). What is the probability, on the second spin, the appearance of the symbol 'B' on the same places where the symbol A appeared on the first spin?
link to original post

So, you want the probability that on the second spin the B symbol will exactly duplicate the pattern of the A symbol on first spin? I'll take a stab at it:

Let your P(A) = a
P(B) = b

Let p(n) be the probability that the A symbol appears n times on the first spin, and that the second spin results in a pattern of B symbols that exactly match the A symbol pattern of the first spin.

Then p(n) = aⁿ * (1-a)^(15-n) * c(15,n) * bⁿ * (1-b)^(15-n)

where c(m,n) is the combination function.

and, the total probability of this event occurring is: Σ p(n) where the summation is over n = 0 to 15.

I would appreciate it if other forum members review this, since I'm human and seem to make more than my share of mistakes.
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