Tree Diagrams WALT complete a probability tree diagram

Tree Diagrams WALT complete a probability tree diagram for independent events. Starter Draw a sample space diagram to show the possibilities when you flip 2 coins. What is P(2 Heads)? Coin 2 Coin 1 H T H HH HT T TH TT

Combining Probabilities and What is the probability of rolling a 3 on a fair dice and then rolling a 2 Rolling a 3 Rolling a 2 1 6 x Both 1 36 When combining the probability of two outcomes occurring you multiply their individual probabilities

Combining Probabilities or What is the probability of rolling a 3 on a fair dice or rolling a 2 Rolling a 3 Rolling a 2 1 6 + Both 2 6 When combining the probability of either two outcomes occurring you add their individual probabilities

Combining Probabilities If you see and then multiply the probabilities If you see or then add the probabilities Example Rolling a Dice Probability of rolling a 3 and a 5 Probability of rolling a 3 or a 5

I flip two coins, what is the probability that I get two heads? P(HH) = 1 4 Coin 1 Coin 2 1 2 1 2 Probabilities on each branch add up to 1 Heads P(HH) = 1 x 1 = 1 2 2 4 Heads P(HT) = 1 x 1 = 1 1 2 Tails 1 2 Heads 2 2 4 P(TH) = 1 x 1 = 1 2 2 4 Tails 1 2 Possible outcomes are shown on the end of the branches Tails P(TT) = 1 x 1 = 1 2 2 Multiply along the branches to work out the probabilities 4

Helen passes through 2 sets of traffic lights on her way to work. The probability that she stops at the first set is 0. 3 The probability that she stops at the second set is 0. 2 What is the probability that she has to stop exactly once? = 0. 24 + 0. 14 Lights 1 Lights 2 0. 2 Stops P(SS) = 0. 3 x 0. 2 = 0. 06 0. 8 Doesn’t Stop P(SD) = 0. 3 x 0. 8 = 0. 24 0. 2 Stops P(DS) = 0. 7 x 0. 2 = 0. 14 Doesn’t Stop P(DD) = 0. 7 x 0. 8 = 0. 56 Stops 0. 3 0. 7 Doesn’t Stop = 0. 38 0. 8

I have a bag of sweets, 3 blue and 7 red. I pick one sweet out without looking, eat it and then pick out and eat a second sweet. What is the probability that I eat one blue and one red sweet? 42 7 = 90 15 Sweet 1 Sweet 2 6 9 7 10 3 10 Red P(RR) = 7 x 6 = 42 10 9 90 Red 3 9 Blue 7 9 Red P(RB) = 7 x 3 = 21 10 9 90 P(BR) = 3 x 7 = 21 10 9 90 Blue 2 9 Blue P(BB) = 3 x 2 = 6 10 9 90