Note 6: Tree Diagrams Tree diagrams are useful for listing outcomes of experiments that have two or more successive events the first event is at the end of the first branch the second event is at the end of the second branch etc. the outcomes for the combined events are listed on the right-hand side.

Each branch represents a possible outcome. The probability of some events can also be found using a probability tree.   Branch Each branch represents a possible outcome. A node is a point where a choice is made. Node

Example 1: A bag contains 5 red balls and 3 green balls. A ball is selected and then replaced. A second ball is selected. Find the probability of selecting two green balls P(2 green) R R G x = R G G

Picasso paints all 7 days in the week Example 2: On a Monday or a Thursday, Mr Picasso paints a ‘masterpiece’ with a probability of . On any other day, the probability of producing a masterpiece is . Mr. Picasso never knows what day it is, so what is the probability that on a random day he will produce a masterpiece? Picasso paints all 7 days in the week

M M,T NM M Other Days NM P(masterpiece) =

Studies: Page 508 Exercise 16F