On-Stage Probability

In just a few days, we will have tryouts to see who will get the parts in the play...

that is the event.

There are so many possibilities for who could play the parts... Dorothy, the Tin Man, the Scarecrow, and the Lion...

those are the possible outcomes.

There is a mathematical tool or picture that can help us see all of the possible outcomes...

that is a tree diagram.

Can you guess the name of the play?
EN00359_.WMF (7922 bytes)

For the play,

Yvette (Y) and Zoë (Z)

want to try out for the part of Dorothy.

	One branch of this tree diagram shows... Y = Yvette as a possible outcome. The other branch shows... Z = Zoë as a possible outcome.
That's a total of two possible outcomes for the part of Dorothy. So what is a possible outcome anyway?

So... how many
possible outcomes
are there for the part of Dorothy?

A possible outcome is

a choice

a possibility

the way something could turn out!

Is Cinderella a possible outcome for a part in my play?Yes No
Click on the word to check your answer.

In my play, you could have the part of...

These are the possible outcomes for parts in my play. Click on the part you would like to have.

Andy (A), Bob (B), and Clay (C)
want to try out for the part of the Tin Man.
What are the possible outcomes for the parts of Dorothy and the Tin Man?

Here is a tree diagram that shows the possible outcomes.

How many different possible outcomes are there for the part of Dorothy?

How many different possible outcomes are there for the part of the Tin Man?

Let's look at how a tree diagram works to figure out the possible outcomes.

HINT: Tree diagrams are read from left to right, just like math sentences. Let's go!

PE03555_.WMF (3184 bytes)

Here is just the Y branch of the tree diagram.
HINT: Remember Y stands for Yvette as Dorothy.

If you follow each branch of the tree diagram, you find different possible outcomes for who could get the parts in the play.

wpe5.gif (3223 bytes)
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	Now, you try it. Look at the tree diagram.
Follow each branch of the tree diagram to find each possible outcome for the parts of Dorothy and the Tin Man.

Click on the arrows to show each possible outcome.

(Y, A)

(Y, B)

(Y, C)

How many possible outcomes does the tree diagram show for the parts of Dorothy and the Tin Man altogether?

There is another way to count the number of outcomes.
Here’s how…


2 possibilities for the part of Dorothy... (Y) and (Z)	X	3 possibilities for the part of the Tin Man... (A), (B), and (C)
That makes... 2 X 3

2 x 3 =
possible outcomes for the parts
of Dorothy and the Tin Man.

BL00396_.WMF (3290 bytes)

Dan (D) and Edie (E) SO01181_.WMF (20466 bytes)
want to try out for the part of the Scarecrow.

Now our tree diagram looks like this…

wpe6.gif (3154 bytes)

If Dan (D) and Edie (E) want to try out for the part of the Scarecrow...

How many different possible outcomes are there for the part of just the Scarecrow?

Use the tree diagram to find the possible outcomes for who might be cast as ...

HINT: Remember to... go from left to right and take one branch at a time.

Follow the branches of the tree diagram to predict who might get the parts in the play.

(Y, A, D) is the first possible outcome.

(Y, A, E) is the next one.

( , B, D)

( , B, E)

( , C, D)

( , C, E)

( , , )

Let's add this to the number sentence.
Here’s how…


2 possibilities for the part of Dorothy... (Y) and (Z)	X	3 possibilities for the part of Tin Man... (A), (B), and (C)	X	2 possibilities for the part of Scarecrow... (D) and (E)

That's...

2 X 3 X 2

2 x 3 x 2 = possible outcomes for ...
Dorothy, the Tin Man, AND the Scarecrow.

I need your help to build the Y branch of the tree diagram. Then you can see the possible outcomes.

Click on the arrows to choose the possible outcomes for the part of the Lion. I have done the first few for you. Do you see a pattern?
HINT: Remember to... go from left to right and take one branch at a time.






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You did it! Here is the Y branch of the tree diagram.


Possible Cast

I need your help to predict EACH of the possible outcomes.
Click on the arrow to select.

(Y, A, D, F) is the first possible outcome.

(Y, A, D, G) is the next possible outcome.

(Y, A, E, F)

(Y, A, E, G)

(Y, B, D, )

(Y, B, D, G)

(Y, B, E, )

(Y, C, , )

(Y, , , )

(, , , )

Wow! What a bunch of possibilities I have as director! But it's time for my lunchbreak. How would you like to be my co-director?

Have I got a job for you!

Here's a list... BS00576_.WMF (3090 bytes)

1. The Y branch of the tree diagram is finished
to show the possible outcomes if Yvette gets the
part of Dorothy.

Finish the Z branch of the tree diagram to show the possible outcomes if Zoë (Z) gets the part.

2. Predict and Figure out...
How many different possibilities
are there for the cast? See you in ten!