Tree Diagrams A tree diagram is a diagrammatical

Tree Diagrams • A tree diagram is a diagrammatical way of representing the probabilities of two or more events • To calculate probabilities using a tree diagram, you multiply along the branches

Tree Diagrams • The probability that it will rain on Monday is 0. 2. The probability that it will rain on Tuesday is 0. 3. • What is the probability that it will rain on Monday and Tuesday?

Tuesday Monday 0. 3 It rains Vertically, We drawing know. Look! that the • We can solve this problem by a tree the numbers add up to 1. It rains probability is 0. 2 diagram. 0. 2 There 0. 7 are two. It does not rain Look!Now Vertically, let’s look the at possible events here; rains or It does that itnot rains numbers Tuesday add up to 1. The. Itprobability on rain Tuesday was given to us as rains 0. 3 We can work. Itout that the 0. 8 probability ofand itprobability? not It does Well, What raining is. Look! the Vertically, notraining the has. Mutually to be 0. 7, because they not rain are numbers Exclusive add. Events. up to 1. 1 – 0. 2 = 0. 8 have to probabilities add up to 1. have to So their We now have the add up to 1. 0. 7 required Tree Diagram. It does not rain

We wanted to know the probability that it rained on Monday and Tuesday Monday 0. 3 It rains 0. 7 It does not rain 0. 3 It rains 0. 2 x 0. 3 = 0. 06 It rains 0. 2 0. 8 It does not rain 0. 7 It does not rain We work outpath the that probability ofon both events happening by multiplying the individual This So can the is the probability only through it rains the tree Monday whichand gives Tuesday us rain ison 0. 06 both days probabilities together

Actually, we can work out the probabilities of all the possible events Tuesday Monday 0. 3 It rains 0. 7 It does not rain 0. 2 x 0. 7 = 0. 14 0. 3 It rains 0. 2 0. 8 It does not rain 0. 7 It does not rain The probability of rain on Monday, but no rain on Tuesday is 0. 14

Tuesday Monday 0. 3 It rains 0. 7 It does not rain 0. 3 It rains 0. 2 0. 8 It does not rain 0. 7 0. 8 x 0. 3 = 0. 24 It does not rain The probability that it will not rain on Monday, but will rain on Tuesday is 0. 24

Tuesday Monday 0. 3 It rains 0. 7 It does not rain 0. 3 It rains 0. 7 0. 8 x 0. 7 = 0. 56 It does not rain It rains 0. 2 0. 8 It does not rain The probability that it does not rain on both days is 0. 56

Let’s look at the completed tree diagram Tuesday Monday 0. 3 It rains 0. 06 0. 7 It does not rain 0. 14 0. 3 It rains 0. 24 It rains 0. 2 0. 8 It does not rain 0. 7 0. 56 The end probabilities add up to 1. Remember this! It can help you What your do you notice? check answer! It does not rain

• Amy has a bet with Becky that she can beat her at snooker and pool. • The probability that Amy will win at snooker is ⅗, and the probability she will win at pool is ⅜. a) What is the probability that Amy will win both games? b) What is the probability that Amy will win at least one of the games?