1. Probability & Tree Diagrams

3. A fair coin is flipped 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

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. 10 beads in a bag – 3 Red, 2 Blue, 5 Green.
One taken, returned to bag, then a second taken.
1st
2nd R RR B RB R G RG R BR 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) = 0.3x0.3 = 0.09
0.3
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 R BR
P(BR) = 0.2x0.3 = 0.06
0.3
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 R GR
0.3
P(GR) = 0.5x0.3 = 0.15
0.5 G
0.2 GB B
P(GB) = 0.5x0.2 = 0.10 G GG
0.5
P(GG) = 0.5x0.5 = 0.25
All ADD UP to 1.0

8. Choose a Meal IC AP 0.45 0.55 S F P 0.2 0.45 0.55 IC AP 0.5 0.3 IC AP
Dessert
Ice Cream 0.45
Apple Pie 0.55
Main course
Salad 0.2
Fish & Chips 0.5
Pizza 0.3 IC AP
P(S,IC) = 0.2 x 0.45 = 0.09
0.45
0.55 S F P
P(S,AP) = 0.2 x 0.55 = 0.110
0.2
0.45
0.55 IC AP
P(F,IC) = 0.5 x 0.45 = 0.225
0.5
P(F,AP) = 0.5 x 0.55 = 0.275
0.3 IC AP
P(P,IC) = 0.3 x 0.45 = 0.135
0.45
0.55
P(P,AP) = 0.3 x 0.55 = 0.165