,
where 
are
the basic probabilities of the first symbol occurring and
are
the basic probabilities of the second symbol occurring, on the reels
respectively. 3-reel slot machines
2. Case B – different numbers of stops and symbol distributions on the reels
2.10 A specific symbol three times or another specific symbol twice
The probability of this event is
,
where are
the basic probabilities of the first symbol occurring and
are
the basic probabilities of the second symbol occurring, on the reels
respectively.
Example:
Find the probability of three melons or two cherries occurring on a payline of a 3-reel slot machine having 48, 50, and 56 stops on reels 1, 2, and 3 respectively and the following distributions of the two symbols on these reels respectively: 3, 2, and 2 melons; 2, 1, and 1 cherries.
The basic probabilities are:
and
.
The sought probability is:
.
2.12 A specific symbol three times or another specific symbol at least once
The probability of this event is
,
where are
the basic probabilities of the first symbol occurring and
are
the basic probabilities of the second symbol occurring, on the
reels respectively.
Example:
Find the probability of three sevens or at least one cherry occurring on a payline of a 3-reel slot machine having 80, 80, and 86 stops on reels 1, 2 and 3 respectively and the following distributions of the two symbols on these reels respectively: 3, 2, and 2 sevens; 2, 1, and 1 cherries.
The basic probabilities are:
and
.
The sought probability is:
= 0.049255 = 4.9255%.
2.13 A specific symbol three times or any combination of that symbol with another specific symbol
The
probability of this event is 
,
where are
the basic probabilities of the first symbol occurring and
are
the basic probabilities of the second symbol occurring, on the reels
respectively.
Example:
Find the probability of three red sevens or any combination of a red seven and a blue seven occurring on a payline of a 3-reel slot machine having 45, 47, and 48 stops on reels 1, 2, and 3 respectively and the following distributions of the two symbols on these reels respectively: 3, 2, and 2 red sevens; 2, 2, and 1 blue sevens.
The basic probabilities are:
and
.
The sought probability is:
= 0.000551 = 0.551%.