Tree Diagrams – Conditional – Worksheet The worksheet is provided in a variety of sizes/formats.

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There are 5 red and 3 blue buttons in a bag. What is the probability of picking a red button? 5 8 P (Red) = If I don’t put the button back, what is the probability of picking another red button. 4 7 P (Red) =

a) R R R R R B B B There are 5 red and 3 blue buttons in a sack. A button is taken out and not replaced. Then another button is taken out. What is the probability both buttons are blue? 1st Event 2nd Event Results R R B R B B

b) R R B B B B B B There are 2 red and 6 blue buttons in a sack. A button is taken out and not replaced. Then another button is taken out. What is the probability both buttons are red? What is the probability of choosing at least one red button? 1st Event 2nd Event Results R R B R B B

c) R R R R G G G G G There are 4 red and 5 green buttons in a sack. A button is taken out and not replaced. Then another button is taken out. What is the probability of choosing at least one red button? What is the probability of choosing only one red button? 1st Event 2nd Event Results

d) A science assessment has a practical and written test. Students have an 80% chance of passing the written test. If they pass the written test there is a 60% chance they pass the practical test. If they fail the written test, there is a 30% chance they will pass the practical test. Draw a Probability Tree to show these events. What is the probability a student passes both tests? What is the probability a student passes only one of the tests?

Answers 5 8 x 4 7 = 5 8 x 3 7 = 3 8 x 5 7 = 3 8 x 2 7 = a) R RR R B RB There are 5 red and 3 blue buttons in a sack. A button is taken out and not replaced. Then another button is taken out. What is the probability both buttons are blue? 1st Event 2nd Event Results 4 7 5 8 x 4 7 = 20 56 R RR 5 8 R 5 8 x 3 7 = 15 56 3 7 B RB 5 7 3 8 x 5 7 = 15 56 R BR 3 8 B 3 8 x 2 7 = 6 56 2 7 B BB Answers

Answers 2 8 x 1 7 = 2 8 x 6 7 = 6 8 x 2 7 = 6 8 x 5 7 = b) R RR R B RB There are 2 red and 6 blue buttons in a sack. A button is taken out and not replaced. Then another button is taken out. What is the probability both buttons are red? 2/56 What is the probability of choosing at least one red button? 26/56 1st Event 2nd Event Results 1 7 2 8 x 1 7 = 2 56 R RR 2 8 R 2 8 x 6 7 = 12 56 6 7 B RB 2 7 6 8 x 2 7 = 12 56 R BR 6 8 B 6 8 x 5 7 = 30 56 5 7 B BB Answers

Answers 4 9 x 3 8 = 4 9 x 5 8 = 5 9 x 4 8 = 5 9 x 4 8 = c) RR R R RG G There are 4 red and 5 green buttons in a sack. A button is taken out and not replaced. Then another button is taken out. What is the probability of choosing at least one red button? 52/72 What is the probability of choosing only one red button? 40/72 1st Event 2nd Event Results 4 9 x 3 8 = 12 72 3 8 RR R At least one red: 4 9 12 72 + 20 72 + 20 72 R 4 9 x 5 8 = 20 72 5 8 RG G = 52 72 4 8 5 9 x 4 8 = 20 72 GR R 5 9 G 5 9 x 4 8 = 20 72 4 8 G GG Answers

Answers 4 9 x 3 8 = 4 9 x 5 8 = 5 9 x 4 8 = 5 9 x 4 8 = c) RR R R RG G There are 4 red and 5 green buttons in a sack. A button is taken out and not replaced. Then another button is taken out. What is the probability of choosing at least one red button? 52/72 What is the probability of choosing only one red button? 40/72 1st Event 2nd Event Results 4 9 x 3 8 = 12 72 3 8 RR R Only one red: 4 9 20 72 + 20 72 R 4 9 x 5 8 = 20 72 5 8 RG G = 40 72 4 8 5 9 x 4 8 = 20 72 GR R 5 9 G 5 9 x 4 8 = 20 72 4 8 G GG Answers

0.6 0.8 0.4 0.3 0.2 0.7 Answers d) P PP P F PF P FP F F FF A science assessment has a practical and written test. Students have an 80% chance of passing the written test. If they pass the written test there is a 60% chance they pass the practical test. If they fail the written test, there is a 30% chance they will pass the practical test. Draw a Probability Tree to show these events. What is the probability a student passes both tests? 0.48 What is the probability a student passes only one of the tests? 0.38 Written Test Practical Test Results 0.6 P PP 0.8 x 0.6 = 0.48 P 0.8 0.4 F PF 0.8 x 0.4 = 0.32 0.3 P FP 0.2 x 0.3 = 0.06 0.2 F 0.7 F FF 0.2 x 0.7 = 0.14 Answers

Conditional Tree Diagrams

Conditional Tree Diagrams

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