# Tree diagram to find probability of two or more events

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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
8. Main course Choose a meal Pudding
Ice Cream 0.45