Probability Tree Diagrams GCSE Statistics Probability Tree Diagrams

A tree diagram can be used for combined events. Each branch of the tree represents a possible combination of outcomes. The probability of the outcome is written on the branch. For example, the tree diagram shows the outcome of drawing a ball from a bag containing five red and four green balls, noting it’s colour, replacing it and then drawing a ball and noting it’s colour. ball 1 ball 2 outcome probability 5 9 R RR 5 9 × 5 9 = 25 81 5 9 R 4 9 5 9 × 4 9 = 20 81 G RG 5 9 R GR 4 9 4 9 × 5 9 = 20 81 G 4 9 4 9 × 4 9 = 16 81 G GG Information can then be taken from the tree diagram

the total of these probabilities is 1 G 5 9 4 9 ball 1 ball 2 outcome RR RG GR GG probability 5 9 × 5 9 = 25 81 5 9 × 4 9 = 20 81 4 9 × 5 9 = 20 81 4 9 × 4 9 = 16 81 the total of these probabilities is 1 The probability of getting two balls the same colour P(R and R) + P(G and G) = 25 81 + 16 81 = 41 81 the probability of getting a red and a green ball would be: P(R and G) + P(G and R) = 20 81 + 20 81 = 40 81

2 Independent Events. 3 Selections For the higher tier exam you are expected to deal with tree diagrams that extend to 3 (or more) branches. First Choice Second Choice Third Choice red 2 Independent Events. 3 Selections blue red red red blue blue red red blue blue blue red 3 Ind/3 Select blue

Sometimes one branch may finish earlier than others . The tree diagram shows the probability of drawing a red ball from a bag of 3 black and 1 red ball. You win if you get the red ball. Second Choice 1 4 3 4 R B First Choice 1 4 3 4 R B Third Choice Outcome Probability R = 1 4 BR = 3 4 × 1 4 = 3 16 BBR = 3 4 × 3 4 × 1 4 = 9 64 BBB = 3 4 × 3 4 × 3 4 = 27 64 1 4 3 4 R B

Your turn Exercise 7J page 278