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08 December 201808 December 2018 Combined Events

I’m playing Monopoly and want to land on Park Lane to buy it. I need a 7. What is the probability I roll a 7 on 2 dice? 𝑃 7 = 1 6

Sample Space Diagrams Imagine one dice was red and one was blue. Dice 1 There are 36 equally likely outcomes. + How many ways can we get a 7? 2 3 4 5 6 7 8 9 10 11 12 P(7) = 6 36 = 1 6 Dice 2 1 36 P(12) = 5 36 P(6) = Total Score

+ 2 3 4 5 6 7 8 9 10 11 12 P(8) = P(9) = P(even) = P(0) = Sample Space Diagrams Dice 1 P(8) = + P(9) = 2 3 4 5 6 7 8 9 10 11 12 P(even) = Dice 2 P(0) = P(more than 7) = P(3, 5 or 10) = Total Score

Answers Sample Space Diagrams 5 36 Dice 1 P(8) = + 4 36 = 1 9 P(9) = 2 3 4 5 6 7 8 9 10 11 12 18 36 = 1 2 P(even) = Dice 2 0 36 P(0) = = 0 15 36 = 5 12 P(more than 7) = 9 36 = 1 4 P(3, 5 or 10) = Total Score

2 3 4 1 2 3 4 5 6 1 2 3 4 5 A student makes a hexagonal spinner (1-6) and a pentagonal spinner (1-5). a) Complete the Sample Space Diagram for spinning both and adding their scores. 1st Spinner 1 2 3 4 5 6 2 3 4 1 2 Calculate: 2nd Spinner 3 b) P(11) = 4 c) P(7) = d) P(8 or more) = 5 e) P(4 or 9) = Total Score f) P(the same number on both spinner) =

A student makes a hexagonal spinner (1-6) and a pentagonal spinner (1-5). a) Complete the Sample Space Diagram for spinning both and adding their scores. 1st Spinner 1 2 3 4 5 6 2 3 4 5 6 7 8 9 10 11 1 2 Calculate: 2nd Spinner 1 30 3 b) P(11) = 1 6 4 c) P(7) = 1 3 d) P(8 or more) = 5 1 5 e) P(4 or 9) = Total Score 1 6 Answers f) P(the same number on both spinner) =

H, 1 T, 5 A dice and a coin are thrown at the same time. a) Complete the Sample Space Diagram. Dice 1 2 3 4 5 6 H, 1 T, 5 Head Coin Tail b) Calculate the probability of scoring a 4 on the dice and a heads on the coin. c) Calculate the probability of scoring tails and an odd number on the dice. d) P(Heads and a number greater than 2) = e) P(NOT a 5 and NOT Heads) =

A dice and a coin are thrown at the same time. a) Complete the Sample Space Diagram. Dice 1 2 3 4 5 6 H, 1 H, 2 H, 3 H, 4 H, 5 H, 6 T, 1 T, 2 T, 3 T, 4 T, 5 T, 6 Head Coin Tail 1 12 b) Calculate the probability of scoring a 4 on the dice and a heads on the coin. 1 4 c) Calculate the probability of scoring tails and an odd number on the dice. 1 3 d) P(Heads and a number greater than 2) = 1 3 e) P(NOT a 5 and NOT Heads) = Answers

A 6-sided and a 4-sided die are thrown and the product of their results recorded. a) Complete a Sample Space Diagram. b) P(Even number) = e) P(NOT a prime number) = c) P(less than 10) = f) P(NOT a square number) = d) P(NOT more than 2) = g) P(11) =

Answers A 6-sided and a 4-sided die are thrown and the product of their results recorded. a) Complete a Sample Space Diagram. Dice 1 1 2 3 4 5 6 1 1 2 3 4 5 6 8 10 12 9 15 18 16 20 24 2 Dice 2 3 4 19 24 3 4 b) P(Even number) = e) P(NOT a prime number) = 5 12 19 24 c) P(less than 10) = f) P(NOT a square number) = 1 8 d) P(NOT more than 2) = g) P(11) =

2. 1. 3. 4.

Check your success! I can complete a sample space diagram. I can use a sample space diagram to calculate combined event probabilities. I can answer GCSE questions on combined events.

Check your success! I can complete a sample space diagram. I can use a sample space diagram to calculate combined event probabilities. I can answer GCSE questions on combined events.

Write a text message to a friend describing: How sample space diagrams are used to find probabilities.

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