Tree Diagrams Be able to use a tree

Tree Diagrams §Be able to use a tree diagram to list the possible outcomes from two events. §Be able to calculate probabilities from tree diagrams. §Understand that Mutually Exclusive Events have probabilities which sum to 1.

• The probability that it will rain on Monday is 0. 2. The Probability 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 Look! Vertically, the We know that the • We can solve this problem by drawing a numbers add up to 1. It rains probability is 0. 2 tree diagram. 0. 2 There 0. 7 are two It does not rain Look!Now Vertically, let’s look theat possible events It rainsthat or Itit rains Thehere; probability numbers Tuesday add up to 1. not rain on does Tuesday was given to It rains us as 0. 3. We can work out 0. 3 0. 8 that. What the probability it not It does Well, raining is Look! the and probability? Vertically, notofraining the raining has to be 0. 7, not are Mutually numbers Exclusive add up to 1. 1 – 0. 2 = 0. 8 because they have to add rain Events. So their probabilities up toto 1. add up to 1. We now have the have 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 out path the that probability both events happening multiplying the This So can the is the probability only through it rainsof the on tree Monday whichand gives Tuesday us by rain is on 0. 06 both days individual 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 x 0. 3 = 0. 24 It does not rain 0. 7 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 What do you check yournotice? answer! It does not rain

Time to have a go … • Try the questions from the book. Remember, if you are unsure, you can watch the presentation again at any point during the lesson.