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
Possible Outcomes H T HT H TH T T TT

4. Attach probabilities 1st 2nd H HH P(H,H)=½x½=¼ ½ ½ H ½ T HT
P(H,T)=½x½=¼ H TH
P(T,H)=½x½=¼ T T TT
P(T,T)=½x½=¼
INDEPENDENT EVENTS – 1st spin has no effect on the 2nd spin

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

6. For example – 10 colored beads in a bag – 3 Red, 2 Blue, 5 Green
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.
1st
2nd R RR B RB R G RG R BR
INDEPENDENT EVENTS B B BB G BG R GR G GB B G GG

7. Probabilities 1st 2nd R RR B RB R G RG R BR B B BB G BG R GR G GB B G
P(RR) = 3/10 * 3/10 = 9/100
3/10
2/10 B RB
P(RB) = 3/10 * 2/10 = 6/100 R
3/10
5/10 G RG
P(RG) = 3/10 * 5/10 =15/100 R BR
P(BR) = 2/10 * 3/10 = 6/100
3/10
2/10
2/10 B B BB
P(BB) = 2/10 * 2/10 = 4/100
5/10 G BG
P(BG) = 2/10 * 5/10 = 10/100 R GR
3/10
P(GR) = 5/10 * 3/10 = 15/100
5/10 G
2/10 GB B
P(GB) = 5/10 * 2/10 = 10/100 G GG
5/10
P(GG) = 5/10 * 5/10 = 25/100
All ADD UP to 100/100 = 1

8. For example – 10 colored beads in a bag – 3 Red, 2 Blue, 5 Green
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.
1st
2nd R RR B RB R G RG R BR
DEPENDENT EVENTS B B BB G BG R GR G GB B G GG

9. Probabilities 1st 2nd R RR B RB R G RG R BR B B BB G BG R GR G GB B G