This ppt teaches what is a Tree diagram and how it is used to calculate the probability of two or more events.
1. Probability & Tree Diagrams
2. What are Tree Diagrams • A way of showing the possibilities of two or more events • Simple diagram we use to calculate the probabilities of two or more events
3. For example – a fair coin is spun twice 1st 2nd H HH H T HT Possible Outcomes H TH T T TT
4. Attach probabilities 1st 2nd ½ H HH P(H,H)=½x½=¼ ½ H ½ T HT P(H,T)=½x½=¼ ½ H TH P(T,H)=½x½=¼ ½ T ½ T TT P(T,T)=½x½=¼ INDEPENDENT EVENTS – 1st spin has no effect on the 2nd spin
5. Calculate probabilities 1st 2nd * ½ H HH P(H,H)=½x½=¼ ½ H ½ T HT P(H,T)=½x½=¼ * * ½ H TH P(T,H)=½x½=¼ ½ T ½ T TT P(T,T)=½x½=¼ Probability of at least one Head?
6. For example – 10 coloured beads in a bag – 3 Red, 2 Blue, 5 Green. One taken, colour noted, returned to bag, then a second taken. 1st 2nd R RR B RB R G RG INDEPENDENT EVENTS R BR B B BB G BG R GR G B GB G GG
7. Probabilities 1st 2nd 0.3 R RR P(RR) = 0.3x0.3 = 0.09 0.2 B RB P(RB) = 0.3x0.2 = 0.06 R 0.3 0.5 G RG P(RG) = 0.3x0.5 = 0.15 0.3 R BR P(BR) = 0.2x0.3 = 0.06 0.2 0.2 B B BB P(BB) = 0.2x0.2 = 0.04 0.5 G BG P(BG) = 0.2x0.5 = 0.10 0.3 R GR P(GR) = 0.5x0.3 = 0.15 G 0.2 GB P(GB) = 0.5x0.2 = 0.10 B 0.5 G GG P(GG) = 0.5x0.5 = 0.25 All ADD UP to 1.0
8. Main course Choose a meal Pudding Ice Cream 0.45 Salad 0.2 Apple Pie 0.55 Egg & Chips 0.5 Pizza 0.3 IC P(S,IC) = 0.2 x 0.45 = 0.09 0.45 S 0.55 0.2 AP P(S,AP) = 0.2 x 0.55 = 0.110 0.45 IC P(E,IC) = 0.5 x 0.45 = 0.225 0.5 E 0.55 AP P(E,AP) = 0.5 x 0.55 = 0.275 0.3 IC P(P,IC) = 0.3 x 0.45 = 0.135 P 0.45 0.55 AP P(P,AP) = 0.3 x 0.55 = 0.165
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