Probability Explanation And Exercises Worksheet Page 25
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37n
is the number of times Outcome 1 occurs,
1
n
is the number of times Outcome 2 occurs,
2
n
is the number of times Outcome 3 occurs,
3
p
is the probability of Outcome 1
1
p
is the probability of Outcome 2, and
2
p
is the probability of Outcome 3.
3
For the chess example,
n
= 12 (12 games are played),
n
= 7 (number won by Player A),
1
n
= 2 (number won by Player B),
2
n
= 3 (the number drawn),
3
p
= 0.40 (probability Player A wins)
1
p
= 0.35(probability Player B wins)
2
p
= 0.25(probability of a draw)
3
12!
p =
.40
.7
.35
.2
.25
3
= 0.0248
(7!) (2!) (3!)
The formula for k outcomes is:
12
!
p
=
.
40 35 25
7
.
2
.
3
=
0 0248
.
( !) ( !) ( !)
7
2
3
n!
p
p
p ... p
=
n
n
n
1
2
k
( !) (n !) ... (n !)
n
1
2
k
1
2
k
209
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