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Name: Class/Set: Tree Diagrams - Independent Events www..mathsprint.co.uk 1: A12 spinner has 1 orange section and 4 pink sections (all equal). It is spun twice. Use this tree diagram to answer the following: 1 5 4 5 1 5 orange 4 5 pink 1 5 orange 4 5 pink orange pink a) What is the probability of getting orange twice? ____________________ b) What is the probability of not getting orange twice? ____________________ c) What is the probability of getting the same colour twice? ____________________ d) What is the probability of getting different colours? ____________________ Free worksheet created by MATHSprint. Tree Diagrams - Independent Events:1 MATHSprint, 2013 1 2: The probability of a biased coin landing Heads up is 0.9. 2 It is tossed twice. Complete this tree diagram and hence answer the following: Heads Heads Tails Heads Tails Tails a) What is the probability of getting Tails twice? ____________________ b) What is the probability of not getting Tails twice? ____________________ c) What is the probability of getting the same result twice? ____________________ d) What is the probability of getting Heads exactly once? ____________________ Free worksheet created by MATHSprint. Tree Diagrams - Independent Events:1 MATHSprint, 2013 1 3: The probability of a certain type of TV being faulty is 0.29. 2 Two TVs are selected at random. Complete this tree diagram and hence answer the following: faulty faulty working a) What is the probability of getting two faulty TVs? ____________________ b) What is the probability of not getting two faulty TVs? ____________________ c) What is the probability of getting exactly one faulty TV? ____________________ d) What is the probability of not getting exactly one faulty TV? ____________________ Free worksheet created by MATHSprint. Tree Diagrams - Independent Events:1 MATHSprint, 2013 1 4: One drawer contains 2 blue socks and 7 purple socks. 2 A second drawer contains 3 blue socks and 2 purple socks. A sock is chosen at random from each drawer. Use this tree diagram to answer the following: 2 9 7 9 3 5 blue 2 5 purple 3 5 blue 2 5 purple blue purple a) What is the probability of getting two blue socks? ____________________ b) What is the probability of getting purple at least once? ____________________ c) What is the probability of getting two socks of different colours? ____________________ d) What is the probability of getting two socks of the same colour? ____________________ Free worksheet created by MATHSprint. Tree Diagrams - Independent Events:1 MATHSprint, 2013 1 5: One spinner has 5 black sections and 5 red sections (all equal). 2 Another spinner has 1 black section and 5 red sections (all equal). Complete this tree diagram and hence answer the following: black black red black red red a) What is the probability of getting red twice? ____________________ b) What is the probability of getting black at least once? ____________________ c) What is the probability of getting the same colour twice? ____________________ d) What is the probability of getting different colours? ____________________ Free worksheet created by MATHSprint. Tree Diagrams - Independent Events:1 MATHSprint, 2013 1 6: One box contains 2 white balls and 6 yellow balls. 2 A second box contains 2 white balls and 5 yellow balls. A ball is chosen at random from each box. Complete this tree diagram and hence answer the following: white white yellow a) What is the probability of getting two yellow balls? ____________________ b) What is the probability of getting white at least once? ____________________ c) What is the probability of getting two balls of different colours? ____________________ d) What is the probability of getting two balls of the same colour? ____________________ Free worksheet created by MATHSprint. Tree Diagrams - Independent Events:1 MATHSprint, 2013 Answers: Tree Diagrams - Independent Events www..mathsprint.co.uk 1: 1 2 1 5 4 5 1 5 orange 4 5 pink 1 5 orange 4 5 pink 0.9 Heads 0.1 Tails 0.9 Heads 0.1 Tails orange pink a) p(getting orange twice) = 15 × 15 = 251 b) p(not getting orange twice) = 1 − 15 × 15 = 24 25 c) p(getting the same colour twice) = 15 × 15 + 45 × 45 = 17 25 d) p(getting different colours) = 15 × 45 + 45 × 15 = 258 2: 1 2 0.9 0.1 Heads Tails a) p(getting Tails twice) = 0.1 × 0.1 = 0.01 b) p(not getting Tails twice) = 1 − 0.1 × 0.1 = 0.99 c) p(getting the same result twice) = 0.9 × 0.9 + 0.1 × 0.1 = 0.82 d) p(getting Heads exactly once) = 0.9 × 0.1 + 0.1 × 0.9 = 0.18 Free worksheet created by MATHSprint. Tree Diagrams - Independent Events:1 MATHSprint, 2013 3: 1 2 0.29 0.71 0.29 faulty 0.71 working 0.29 faulty 0.71 working faulty working a) p(getting two faulty TVs) = 0.29 × 0.29 = 0.0841 b) p(not getting two faulty TVs) = 1 − 0.29 × 0.29 = 0.9159 c) p(getting exactly one faulty TV) = 0.29 × 0.71 + 0.71 × 0.29 = 0.4118 d) p(not getting exactly one faulty TV) = 0.29 × 0.29 + 0.71 × 0.71 = 0.5882 4: 1 2 2 9 7 9 3 5 blue 2 5 purple 3 5 blue 2 5 purple blue purple a) p(getting two blue socks) = 29 × 35 = 456 = 152 13 b) p(getting purple at least once) = 1 − 29 × 35 = 39 45 = 15 5 c) p(getting two socks of different colours) = 29 × 25 + 79 × 35 = 25 45 = 9 4 d) p(getting two socks of the same colour) = 29 × 35 + 79 × 25 = 20 45 = 9 5: 1 2 5 10 5 10 1 6 black 5 6 red 1 6 black 5 6 red black red 5 a) p(getting red twice) = 105 × 56 = 25 60 = 12 Free worksheet created by MATHSprint. Tree Diagrams - Independent Events:1 MATHSprint, 2013 b) p(getting black at least once) = 1 − 5 10 7 × 56 = 35 60 = 12 c) p(getting the same colour twice) = 105 × 16 + d) p(getting different colours) = 105 × 56 + 6: 5 10 5 10 1 × 56 = 30 60 = 2 1 × 16 = 30 60 = 2 1 2 2 8 6 8 2 7 white 5 7 yellow 2 7 white 5 7 yellow white yellow 15 a) p(getting two yellow balls) = 68 × 57 = 30 56 = 28 13 b) p(getting white at least once) = 1 − 68 × 57 = 26 56 = 28 11 c) p(getting two balls of different colours) = 28 × 57 + 68 × 27 = 22 56 = 28 17 d) p(getting two balls of the same colour) = 28 × 27 + 68 × 57 = 34 56 = 28 Free worksheet created by MATHSprint. Tree Diagrams - Independent Events:1 MATHSprint, 2013