Example 1
A spinner has three different colours red (x3), blue (x2) and green (x2). Find:
a) P (Red & Blue)
b) P (At Least 1 Blue)
a) We need to find ways to get red & blue. There are two possibilities either Red (1) & Blue (2) or Blue (1) & Red (2). To find the
probability of these combined events, we need to multiply the probabilities of red and blue and blue and red. Using the tree diagram we
have found the combined probability (working out in the red boxes). Since both combined events are the same (just the other way
around), the answers are identical. Now we simply need to add together the two results to see how likely both of these possibilities are
to happen.
The solution is P (red & blue) = 12/49
b) We need to find all the ways to get at least one blue. These are:
•
RB
•
BR
•
BB
•
BG
•
GB
We need to find the probability of all these combined events. The working out is in the blue boxes. Now we simply need to add all these
combined probabilities together.

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0.333...

0.444...

0.222...

Spin 1 (1)

Spin 2 (2)

Example 2
We now have a bag with 12 marbles (2 red, 4 blue, 6 green). We have to pick twice (replacing the marble each time) Find:
a) P (Same Colour Twice)
b) P (Not Blue)
a) To find the answer to part a we have to look at all the possibilities where we get the same colour twice: RED & RED, BLUE & BLUE
and GREEN & GREEN. We then have to calculate the probabilities for these combined events (working out in the red boxes). Lastly, we
have to add these probabilities.
The solution is P (Same Colour Twice) = 14/36
b) We need to find all the possibilities that do not contain blue. These are:
•
RR
•
RG
•
GR
•
GG
We need to find the probability of all these combined events. The working out is in the blue boxes. Now we simply need to add all these
combined probabilities together.
The solution is P (Not Blue) = 16/36

Pick 1 (1)

Pick 2 (2)

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Chapter 21.2: Learning Outcomes
Students will learn how to calculate the probability of single events!
Students will learn how to use and interpret tree diagrams!
Students will learn how to calculate the probability of combined events!

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