Probability
by Joe McDonald
Let us roll 2 die one at a time...
Recall, there are 6 sides to a die
so there are six elements in the sample space
An experiment (craps) consists of throwing two
dice, one red and one green, and observing the uppermost face. Notice, there are 6 sides
of each die. The possible different rolls would 6
× 6 = 6² = 36 outcomes. The reason for using 2 different color dice is
to emphasize that
(1,2)
and (2,1)
are 2 different throws.
Here is the sample space... 
occurrences  sum  sum  occurrences  
1  2  (1,1)  (1,2)  (1,3)  (1,4)  (1,5)  (1,6)  
2  3  (2,1)  (2,2)  (2,3)  (2,4)  (2,5)  (2,6)  8  5 
3  4  (3,1)  (3,2)  (3,3)  (3,4)  (3,5)  (3,6)  9  4 
4  5  (4,1)  (4,2)  (4,3)  (4,4)  (4,5)  (4,6)  10  3 
5  6  (5,1)  (5,2)  (5,3)  (5,4)  (5,5)  (5,6)  11  2 
6  7  (6,1)  (6,2)  (6,3)  (6,4)  (6,5)  (6,6)  12  1 
Notice, there are exactly 1 way 2 throw a 2, 2 ways to throw a 3, 3 ways to throw a 4, etc...
Pr( 7 ) = 6 / 36 = 1 / 6 since there are exactly 6 ways to throw a 7 and there are 36 different outcomes in the sample space. How does this relate to the individual throws?

Let us roll 2 die one at a time...
Tutorials and Applets by
Joe McDonald
Community College of Southern Nevada