PS - Probability Diagrams Lesson

Probability Diagrams

As you have probably been told before, "drawing a picture" is often a good problem solving strategy. But how can you draw a picture of probability? In this lesson, you will learn about three ways of organizing data so that you can better see your intersections, unions and probabilities.  

Venn Diagrams

The next type of diagram we will look at will be a Venn diagram. You have probably seen these before, but here is a quick reminder of how they work. 

Now, consider the following situation:

A class participates in a survey to find out whether students like Hip Hop or Country music.

Each student came up to the board and put their initials into the following chart.  The bolded students like both types of music.

Hip Hop (HH)	Country (C)	Neither (N)
BHO	BHO	RWR
WJC	GWB	GRF
RMN	GHB	HST
JFK	JEC
DDE	RMN
WGH	LBJ
WHT	DDE
	FDR
	HCH
	WGH

Now copy the following Venn diagram on your own paper and write the students' initials where they belong in the diagram

Where did you put everyone? Check your Venn diagram below. Be sure to correct your paper copy. You will be using it again.

Two-Way Tables

Last you will learn about two way tables. Two way tables are helpful because you can see all of your groups, how much they intersect, and what your totals are, all in one table. We will take a look at the vending machine data from the Tree diagram video. This time, it will be in a two way table.

Should we change the vending machines?

	Yes	No	Total
Upper-classmen	300	100	400
Under-classmen	450	150	600
Total	750	250	1000

There are a few important things to notice about our two way table.

• We have one outcome listed across the top (YES / NO) and the other listed down the left side (UPPER / UNDER).
• We have totals listed at the end of each row and column, and then a grand total in the lower right corner.
• Every row will sum up to its total, as will every column.
• Where a row and column intersect is where their data intersect.

1. How many students were polled?

• Solution: 1000

2. How many upper classmen were polled?

• Solution: 400

3. How many upper classmen said yes?

• Solution: 300

4. How many students said yes?

• Solution: 750

5. How many under classmen said no?

• Solution: 150

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