1. Independence and Tree Diagrams Slideshow 56, Mathematics Mr Richard Sasaki, Room 307

2. Objectives Review multiplying decimal numbers less than 1 Learn some new notation about different events Recall how to make calculations with independent events Introduce Tree Diagrams

3. Decimal Numbers We will start using decimal numbers in probability (as well as fractions). Let’s have a bit of practice multiplying and dividing some!

4. 0.030.18 0.210.42 0.0210.092 0.0045 0.07 0.50.3 0.90.3 0.1250.08 0.010.375

5. Notation Do you remember how to calculate the probability of two independent events occurring successfully? Example We roll an unbiased regular die and a spin an unbiased spinner with values 1, 2 and 3 in that order. What is the probability of getting a 5 and then a 2? P(5, 2) =

6. Notation When independent events take place, we multiply both of their probabilities to find the probability of them both occurring. Note – This is only true when events A and B are independent! Also, the complement of A is written A’. Do you remember how to write “the probability of event A and B”?

7. P(A’) = 0.6 Replacing / with replacement) Because P(B) = P(B’) = ½

8. Tree Diagrams We can represent different possible outcomes with tree diagrams. Branches represent independent events. Let’s consider two events with only success and fail outcomes. Event AEvent B P(A) P(A’) P(B) P(B’) P(B) P(B’)

9. Example Event A Event B P(A) P(A’) P(B) P(B’) P(B) P(B’) 0.3 0.7 0.9 0.1 =0.03 =0.07

10. Answers - Easy Because So A and B must be independent.

11. Answers - Hard A B P(Other)