Probability Tree Diagrams What are Tree Diagrams A
Probability & Tree Diagrams
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
For example – a fair coin is spun twice 1 st 2 nd H HH T HT H TH T TT H T Possible Outcomes
Attach probabilities 1 st ½ ½ 2 nd ½ H H HH P(H, H)=½x½=¼ T HT P(H, T)=½x½=¼ ½ H TH P(T, H)=½x½=¼ ½ T TT P(T, T)=½x½=¼ ½ T INDEPENDENT EVENTS – 1 st spin has no effect on the 2 nd spin
Calculate probabilities 1 st ½ ½ 2 nd ½ H H HH P(H, H)=½x½=¼ * T HT P(H, T)=½x½=¼ ½ H TH P(T, H)=½x½=¼ * * ½ T TT P(T, T)=½x½=¼ ½ T Probability of at least one Head?
For example – 10 colored beads in a bag – 3 Red, 2 Blue, 5 Green. One taken, color noted, returned to bag, then a second taken. 1 st 2 nd R B G R RR B RB G R RG BR B BB G R BG GR B GB G GG INDEPENDENT EVENTS
Probabilities 1 st 3/10 2 nd R R 3/10 2/10 RR P(RR) = 3/10 * 3/10 = 9/100 B RB P(RB) = 3/10 * 2/10 = 6/100 G R RG BR P(RG) = 3/10 * 5/10 =15/100 P(BR) = 2/10 * 3/10 = 6/100 B BB P(BB) = 2/10 * 2/10 = 4/100 G R BG GR P(BG) = 2/10 * 5/10 = 10/100 P(GR) = 5/10 * 3/10 = 15/100 B GB P(GB) = 5/10 * 2/10 = 10/100 G GG P(GG) = 5/10 * 5/10 = 25/100 5/10 3/10 2/10 B 2/10 5/10 G 3/10 2/10 5/10 All ADD UP to 100/100 = 1
For example – 10 colored beads in a bag – 3 Red, 2 Blue, 5 Green. One taken, color noted, not returned to bag, then a second taken. 1 st 2 nd R B G R RR B RB G R RG BR B BB G R BG GR B GB G GG DEPENDENT EVENTS
Probabilities 1 st 2 nd R B G R RR B RB G R RG BR B BB G R BG GR B GB G GG
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