Tree Diagrams – Unconditional – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.

John flips a coin and Jane rolls a dice. These are independent events. What is the probability the result is tails and a 6? Coin Flip Dice Roll Results 1 6 1 2 × 1 6 = 1 12 6 H6 Heads AND a 6 H 1 2 5 6 1 2 × 5 6 = 5 12 1-5 H1-5 1 6 1 2 × 1 6 = 1 12 6 T6 1 2 T 5 6 1 2 × 5 6 = 5 12 1-5 T1-5

Unconditional Tree Diagrams To win the league, Burham United need to win against Wedly Wanderers & then Rexham Rovers. Unconditional Tree Diagrams ① The probability of winning again Wedly is 2 3 The probability of winning again Rexham is 3 4 What is the probability Burham win the league (win both matches)? Vs. Wedley Vs. Rexham Result 3 4 2 3 × 3 4 = 6 12 P(WW) = 6 12 Win WW 2 3 Win 2 3 × 1 4 = 2 12 1 4 Lose WL 3 4 1 3 × 3 4 = 3 12 Win LW 1 3 Lose 1 3 × 1 4 = 1 12 1 4 Lose LL

The probability it is sunny on Saturday is 3 7 ② The probability it is sunny on Sunday is 2 5 What is P(not sunny all weekend)? Saturday Sunday Result 2 5 3 7 × 2 5 = 6 35 Sunny SS 3 7 Sunny 3 7 × 3 5 = 9 35 3 5 Not Sunny SN 2 5 4 7 × 2 5 = 8 35 Sunny NS 4 7 Not Sunny 4 7 × 3 5 = 12 35 3 5 Not Sunny P(NN) = 12 35 NN

There are black and white marbles in the box. ③ Box & Marbles One is picked – and replaced – then another is picked. What is the probability both picks are the same colour? P (BB or WW) = 9 100 + 49 100 = 58 100 1st Pick 2nd Pick Result 3 10 3 10 × 3 10 = 9 100 Black BB 3 10 Black 3 10 × 7 10 = 21 100 7 10 White BW 3 10 7 10 × 3 10 = 21 100 Black WB 7 10 White 7 10 × 7 10 = 49 100 7 10 White WW

④ The probability Jill passes her Geography test is 0.8 The probability Jill passes her Science test is 0.4 What is the probability she passes only one of the tests? P(PF or FP) = 0.48+0.08 = 0.56 Geography Test Science Test Result 0.4 Pass PP 0.8 ×0.4=0.32 Pass 0.8 0.6 Fail PF 0.8 ×0.6=0.48 0.4 Pass FP 0.2 ×0.4=0.08 0.2 Fail Fail FF 0.2 ×0.6=0.12 0.6

A coin and a dice were thrown. What is the possibility of getting a Tails and a 6? What did Mary do wrong? 1st Event 2nd Event Results 1 6 1 2 x 1 6 = 1 12 1-5 T1-5 1 2 T 1 2 x 1 6 = 2 12 1 6 6 T6 5 6 1 2 x 5 6 = 6 12 1-5 H1-5 1 2 H 1 2 x 5 6 = 5 12 5 6 6 H6

A coin and a dice were thrown. What is the possibility of getting a Tails and a 6? What did Mary do wrong? 1st Event 2nd Event Results 1 6 1 2 x 1 6 = 1 12 1-5 T1-5 1 2 T 1 2 x 1 6 = 2 12 1 6 6 T6 5 6 1 2 x 5 6 = 6 12 1-5 H1-5 1 2 H 1 2 x 5 6 = 5 12 5 6 6 H6

tom@goteachmaths.co.uk Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths.co.uk