Check P189 Master Strengthen P191 Extend P195 Test P199 8.5 Probability diagrams You will learn to: Why learn this? You can use probabilities of two events, like rolling two dice, to work out strategies for games like Yahtzee or backgammon. Fluency • You roll an ordinary fair dice. What is P(5) P(even number) P(at least 3)? • In 30 rolls, how many 2s would you expect? Explore How likely are you to roll a double with two dice? Exercise 8.5 8 1 For this spinner, what is a P(red) b P(blue) c P(red or blue) d P(red and even) 1 7 2 6 3 5 e P(blue and odd)? Warm up CONFIDENCE • List all the possible outcomes of one or two events in sample space diagrams or Venn diagrams • Calculate probabilities of repeated events. 4 2 A 5p and 10p coin are flipped at the same time. a Make a list of the possible outcomes. b How many possible outcomes are there altogether? c Work out i P(two heads) ii P(a head or a tail) Discussion What assumptions do you need to make to answer part c? Q2a hint Organise the outcomes so that you don’t miss any. For example: 5p 10p H H 3 Maria rolls a dice and flips a coin. Copy the sample space diagram. H 1 T H, 1 2 T, 2 3 4 5 Key point A sample space diagram shows all the possible outcomes of two events. 6 a Write in the possible outcomes. How many possible outcomes are there altogether? b Work out i P(an even number and a tail) ii P(3) iii P(a number greater than 4 and a head) Q3b ii hint With head or tail. Unit 8 Probability 184