CK-12-Basic Probability and Statistics Concepts - A Full Course

http://www.ck12.org Chapter 3. Introduction to Discrete Random Variables

It is important to remember that the values of a discrete random variable are not mutually inclusive. Think back to
our car example with Jack and his mom. Jack could not, realistically, find a car that is both a Ford and a Mercedes
(assuming he did not see a home-built car). He would either see a Ford or not see a Ford as he went from his car to
the mall doors. Therefore, the values for the variable are mutually exclusive. Now let’s look at an example.

Example A

Say you are going to toss 2 coins. Show the probability distribution for this toss.

Let the variableXbe the number of times your coin lands on tails. The table below lists all of the possible events
that can occur from the tosses.

TABLE3.5:

Toss First Coin Second Coin X

1 H H 0

2 H T 1

3 T T 2

4 T H 1

We can add a fifth column to the table above to show the probability of each of these events (the tossing of the 2
coins).

TABLE3.6:

Toss First Coin Second Coin X P(X)

1 H H (^014)
2 H T (^114)
3 T T (^214)
4 T H (^114)
As you can see in the table, each event has an equally likely chance of occurring. You can see this by looking at
the columnP(X). From here, we can find the probability distribution. In theXcolumn, we have 3 possible discrete
values for this variable: 0, 1, and 2.
P( 0 ) =toss 1=

1

4

P( 1 ) =toss 2+toss 4

=

1

4

+

1

4

=

1

2

P( 2 ) =toss 3=

1

4

Example B

Represent the probability distribution from Example A graphically.

Now we can represent the probability distribution with a graph, called a histogram. Ahistogramis a graph that uses
bars vertically arranged to display data. Using the TI-84 PLUS calculator, we can draw the histogram to represent