Probability Tree Diagrams In probability tree diagrams as
Probability Tree Diagrams �In probability tree diagrams as in possibility space diagrams we draw up possible outcomes of combined events and find the combined probabilities �A tree diagram gives more information and can show more than 2 events! �In a probability tree diagram we can observe a mixture of mutually exclusive and independent events �We will not be covering dependent events
Probability Tree Diagrams L. O. complete a probability tree diagram for independent events. Starter Draw a possibility space diagram to show the possibilities when you flip 2 coins. What is P(2 Heads)? Coin 2 Coin 1 H T H (H, H)(H, T) T (T, H) (T, T)
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
Rebecca has nine coloured beads in a bag. Four of the beads are black and the rest are green. She removes a bead at random from the bag and notes the colour before replacing it. She then chooses a second bead. (a) Draw a tree diagram showing all possible outcomes. (b)Calculate the probability that Rebecca chooses: (i) 2 green beads (ii) A black followed by a green bead Second Choice First Choice black green
Homework STP 9 Pg 72 No. 1, 2 and 3 �Probabilities of mutually exclusive events add up to 1 �Multiply along the branches � 2 nd level same branches set
c) 7 20 No. 1 Getting to work Leaving work 3 5 7 8 1 8 Probabilities on each branch add up to 1 on time d) 3 40 on time 2 5 late 3 5 on time P(TL) = 7 x 2 = 14 = 7 8 5 40 20 P(LT) = 1 x 3 = 3 late 8 2 5 5 40 late THE SAME PAIR OF BRANCHES Multiply along the branches to work out the probabilities
No. 2 Second Pin First Pin 0. 2 Probabilities on each branch add up to 1 UP P(both Up) = 0. 2 x 0. 2 = 0. 04 UP 0. 8 0. 2 0. 8 d) 0. 64 c) 0. 04 Down UP Down 0. 8 Down THE SAME PAIR OF BRANCHES P(both down) = 0. 8 x 0. 8 = 0. 64 Multiply along the branches to work out the probabilities
No. 3 Second Box First Box 2 5 1 3 2 3 Probabilities on each branch add up to 1 d) 2 15 c) 2 5 lime P(WL) = 1 x 2 = 2 5 3 15 white 3 5 yellow 2 5 lime yellow 3 5 yellow THE SAME PAIR OF BRANCHES P(Both Y) = 2 x 3 = 6 = 2 3 5 15 Multiply along the branches to work out the probabilities 5
Remember �When we move along branches to find the probability of this AND this we multiply the individual probabilities! �For independent events: the two sets of branches on the second level are the same BECAUSE �No matter what happens in the first event – the possible outcomes of the second event will be the same
- Slides: 9