3 Jan and Flavia play draughts. They play two games. The result of the first game does not affect the result of the second game. a Copy and complete the tree diagram. b Work out the probability that 1st game 2nd game 2 5 Jan Jan 2 5 Flavia Jan 3 5 i Jan wins both games Flavia ii Flavia wins both games 3 5 iii Jan and Flavia win one game each. Q3a hint The second game results are independent of the first game results. So each pair of branches for the second game is the same as for the first game. Flavia 4 4 red and 2 blue counters are placed inside a bag. One of the counters is removed from the bag. 1st counter 2nd counter R R R R R R B B R R R R B B B R B B a What is the probability that the counter is i red ii blue? b The first counter is not replaced. How many counters are left in the bag? c Copy and complete the tree diagram. d Work out the probability that i both counters are red ii both counters are blue iii the counters are different colours. Enrichment 1 a Sketch five 8-sided fair spinners like this. b Fill in the sectors with any numbers between 1 and 8, so that: 1 Spinner 1 P(5) = 2 1 Spinner 2 P(less than 3) = 4 3 Spinner 3 P(not a 6) = 8 5 Spinner 4 P(2 or 7) = 8 3 2 Reflect In these strengthen lessons you have answered probability questions that use • Venn diagrams • sample space diagrams • two-way tables • tree diagrams. Which types of question were easiest? Why? Which types of question were hardest? Why? Write down one thing about probability you think you need more practice on. Reflect Spinner 5 P(at least 4) = 4 Unit 8 Probability 194