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Probability & Tree Diagrams

Probability & Tree Diagrams. Possible Outcomes. For example – a fair coin is spun twice. 1 st. 2 nd. H. HH. H. T. HT. H. TH. T. T. TT. Attach probabilities. 1 st. 2 nd. H. HH. P(H,H)= ½x½=¼. ½. H. ½. ½. T. HT. P(H,T)= ½x½=¼. H. TH. ½. P(T,H)= ½x½=¼. ½. T. ½. T.

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Probability & Tree Diagrams

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  1. Probability & Tree Diagrams

  2. Possible Outcomes For example – a fair coin is spun twice 1st 2nd H HH H T HT H TH T T TT

  3. Attach probabilities 1st 2nd H HH P(H,H)=½x½=¼ ½ H ½ ½ T HT P(H,T)=½x½=¼ H TH ½ 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

  4. Calculate probabilities 1st 2nd * H HH P(H,H)=½x½=¼ ½ H ½ ½ * T HT P(H,T)=½x½=¼ * H TH ½ P(T,H)=½x½=¼ ½ T ½ T TT P(T,T)=½x½=¼ Probability of at least one Head?

  5. 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 BB B B G BG R GR G GB B G GG

  6. All ADD UP to 1.0 Probabilities 1st 2nd R RR P(RR) = 0.3x0.3 = 0.09 0.3 0.2 B RB P(RB) = 0.3x0.2 = 0.06 R 0.3 G 0.5 RG P(RG) = 0.3x0.5 = 0.15 R BR P(BR) = 0.2x0.3 = 0.06 0.3 0.2 0.2 BB P(BB) = 0.2x0.2 = 0.04 B B 0.5 G BG P(BG) = 0.2x0.5 = 0.10 R GR P(GR) = 0.5x0.3 = 0.15 0.3 0.5 G 0.2 GB P(GB) = 0.5x0.2 = 0.10 B G GG P(GG) = 0.5x0.5 = 0.25 0.5

  7. IC 0.45 S 0.55 AP IC 0.45 E 0.55 AP IC 0.45 P 0.55 AP Choose a meal Pudding Ice Cream 0.45 Apple Pie 0.55 Main course Salad 0.2 Egg & Chips 0.5 Pizza 0.3 P(S,IC) = 0.2 x 0.45 = 0.09 P(S,AP) = 0.2 x 0.55 = 0.110 0.2 P(E,IC) = 0.5 x 0.45 = 0.225 0.5 P(E,AP) = 0.5 x 0.55 = 0.275 0.3 P(P,IC) = 0.3 x 0.45 = 0.135 P(P,AP) = 0.3 x 0.55 = 0.165

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