1. Probability Tree Diagrams

2. Can be used to show the outcomes of two or more events. Each Branch represents the possible outcome of one event. Probability of each is written on the branch. Final result depends on path taken through the tree

3. Example The probability that a new company will fail in the first 5 years is 0.6. Two new companies are chosen at random a.Show possible outcomes on a tree diagram b.Use diagram to find probability that both will fail c.Find probability that only one fails.

4. Example fail Not fail fail Not fail 1 st Company 2nd Company 0.6 Not fail

5. Example (cont) a.First set of branches shows possible outcomes to first company. Second set shows outcomes for second company. b.The top (blue) path is for the outcome both companies fail P (both fail) = 0.6 x 0.6 = 0.36

6. Example (cont) c.Only one company can fail by two ways – First fails or Second Fail P(Only first fails) = 0.6 x 0.4 = 0.24 P(Only second fails) = 0.4 x 0.6 = 0.24 Therefore only one fails is: P(Only first fails OR Only Second Fails) = 0.24 + 0.24 = 0.48