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Chapter 11 - School District #35

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Name: ___________________________________________________ Date: ______________<br />

Working Example 2: Calculating Probabilities Using a Tree Diagram and<br />

Multiplication<br />

Jason rolls a 4-sided die and spins the spinner.<br />

What is the probability of rolling an even number and spinning a B?<br />

Show your answer using a tree diagram and multiplication.<br />

Solution<br />

Tree Diagram:<br />

2<br />

3<br />

A<br />

C<br />

B<br />

Die<br />

Spinner<br />

Outcomes<br />

There are<br />

possible outcomes.<br />

1<br />

A<br />

B<br />

C<br />

1, A<br />

1, B<br />

1, C<br />

There are<br />

favourable<br />

outcomes (look for even numbers with Bs).<br />

2<br />

Even numbers end in<br />

0, 2, 4, 6, …<br />

P (even number and B) =<br />

favourable outcomes<br />

possible outcomes<br />

=<br />

Multiplication:<br />

favourable outcomes<br />

Die: P (even number) =<br />

Spinner: P (B) =<br />

possible outcomes<br />

favourable outcomes<br />

possible outcomes<br />

=<br />

4<br />

P(even number, B) = P(even number) × P(B)<br />

=<br />

3<br />

= ×<br />

4 3<br />

=<br />

614 MHR ● <strong>Chapter</strong> <strong>11</strong>: Probability<br />

Both methods give the same result.

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