©G Dear2009 – Not to be sold/Free to use General Mathematic (HSC) Multi-Stage Events Probability Trees Stage 6 - Year 12 Press Ctrl-A ©G Dear2009 – Not to be sold/Free to use

Probability Trees We draw a marble from a bag that contains two  green, a blue and a red marble. 1  2 Green 3  4 5 6  P(Green,Even) = 6 24 1  2 1 = and roll a die. Green 3  4 4 5  6 1 2 3 What is the probability of getting a green and an even number? Blue 4 5 6 1 2 3 Red 4 5 6 End of Slide

Probability Trees A better way Green Green 2 4 1 Blue 4 Blue 1 4 Red 3 4 5 6 Green Blue Red 1 2 Odd Green 2 4 1 2 Even 1 2 Odd 1 4 Blue 1 2 Even 1 4 1 2 Odd Red 1 2 Even End of Slide

Multiply along the branches. Probability Trees Multiply along the branches. Odd Green Blue Red Even 2 4 1 A better way 2 P(Green,Even) = 8 2 4 1 2 2 8 1 x = = 4 We draw a marble from a bag that contains two green, a blue and a red marble and roll a die. What is the probability of getting a green and an even number? End of Slide

Multiply along the branches. Probability Trees What is the probability of a Green or Red and an Even Number? Odd Green Blue Red Even 2 4 1 Multiply along the branches. Add Branches together. 2 4 1 2 2 8 x = P(G,R,Even) = 2 8 1 8 + 3 8 = 1 4 1 2 1 8 x = End of Slide

6 6 Not 6 Not Not Probability Trees A game requires a ‘Double-Six’ to start. What is the probability of a ‘Double-Six’? 1 6 1 6 1 6 1 36 6 = X 1 6 6 5 6 Not 1 36 P(6,6) = 1 6 6 5 6 Not 5 6 Not End of Slide

What is the probability of a ‘Only One Six’? Probability Trees What is the probability of a ‘Only One Six’? 1 6 5 36 5 36 6 P(Only One Six) = + 1 6 6 10 36 5 6 1 6 5 6 5 36 = Not = X 5 18 = 1 6 5 6 1 6 5 36 6 = X 5 6 Not 5 6 Not End of Slide

Probability Trees with Replacement A standard pack of cards has 52 cards. 13  13  13  13  Two Cards are chosen and replaced. What is the probability of 2 red cards? Red. 26 52 26 52 26 52 P(Red,Red) = x Red. 26 52 1 4 26 52 = Black Red. 26 52 26 52 Black 26 52 End of Slide Black

Trees -Without Replacement A standard pack of cards has 52 cards. 13  13  13  13  Two Cards are chosen and NOT replaced. What is the probability of 2 red cards? Red. 25 51 26 52 25 51 P(Red,Red) = x Red. 26 52 25 102 26 51 = Black Red. 26 51 26 52 Black 25 51 End of Show Black