Find the expected number of 1's when three fair dice are thrown.
We need the probability of getting: one 1, two 1's, three 1's.
There are: . possible outcomes.
To get three 1's:
There is one way to get three 1's.
To get two 1's:
There are three cases: .[tex]33x, \;3x3,\;x33[/maTH]
. . And there are 5 choices for the third die.
There are: . ways to get two 1's.
To get one 1:
There are three cases: .
. . And there are choices for the other two dice.
There are: . ways to get one 1.