**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%.