Probability Tree diagrams

1. Probability Tree diagrams Example A coin is tossed twice. Complete the probability tree diagram showing all the possible outcomes and the probability of each. What is the probability of the two tosses giving the same result? 1st throw 2nd throw Head Head, Head Head Tail Head, Tail Head Tail, Head Tail Tail Tail, Tail

2. Example A six sided dice is thrown twice. Complete the tree diagram showing all the probabilities 1st throw 2nd throw four four, four four Not four four, Not four Four Not four, four Not 4 Not four Not four, Not four • What is the probability of throwing a total of • two fours? • No fours? • At least one four?

3. First Firework second Firework Lights Lights Fails Lights Fails Fails Example It is found that the probability of a particular brand of firework will not light is . John buys two. Copy and complete the tree diagram and use it to find the probability that both of his fireworks light.

4. Example When cultivating fruit bushes by planting cuttings the probability that a cutting produces a bush is 3/5. Find the probabilities of 0, 1, 2 bushes being produced, if two cuttings are planted. 1st cutting 2nd cutting Bush Bush, Bush Bush No Bush Bush, No Bush Bush No Bush, Bush No Bush No Bush No Bush, No Bush

5. Example • A box contains seven red and three blue pens. Jane takes a pen from the box and keeps it; then Susan takes a pen from the box. Both girls make their selection without looking at the colour. • Draw a tree diagram to show the possible colours each has selected. • Use your tree diagram to find the probability that Jane and • Susan • (i) each select a red pen • (ii) select pens of the same colour.