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Uncertainty


Tree diagrams are used to display all possible outcomes of experiments involving more than one event.

Tree diagram: possible outcomes

You need to decide on your snack. You can have white or chocolate milk to drink. To eat you can have chocolate chip or oatmeal cookies. How many different choices do you have?

Combinations Drinks  

Cookies

Possible Outcomes

 

2

x

2

4

Example:

In an experiment, Philip flips two counters. One side of each counter is blue and the other is red. Find all possible outcomes. What is the probability of both counters landing blue side up?

You can use a tree diagram to show all possible outcomes.

Event 1 Event 2 Outcomes Write
First Counter Second Counter    
       
Blue (B)

Blue (B)

Blue, Blue

(B, B)
 

Red (R)

Blue, Red

(B, R)
Red (R)

Blue (B)

Red, Blue

(R, B)
 

Red (R)

Red, Red

(R, R)
       
Probability of both blue P (B, B) = 1/4 1favorable outcomes
4 possible outcomes
There are 4 possible outcomes.
The probability of both counters landing blue side up is 1/4.
 

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Remember:

A tree diagram looks like branches of a tree.
The order does not change the number of outcomes in a tree diagram.

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