Hello, helloworld101!

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[/tex]

. . 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.

. .