Answer: 0.71
Step-by-step explanation:
A="The policyholder needs Orthodontics"
B="The policyholder needs filling"
C="The policyholder needs extraction"
P(A)=1/2, P(AUB)=2/3, P(AUC)=3/4, P(B∩C)=1/8
The events are independents, so:
P(A∩B)=P(A)P(B), P(A∩C)=P(A)P(C) and P(B∩C)=P(B)P(C)
P(AUB) = P(A)+P(B)-P(A∩B) = P(A)+P(B)+P(A)P(B)
2/3=1/2+P(B)-1/2*P(B), P(B)=1/3
P(AUC) = P(A)+P(C)-P(A∩C) = P(A)+P(C)+P(A)P(C)
3/4=1/2+P(C)-1/2*P(C), P(C)=1/2
P(BUC)=P(B)+P(C)-P(B∩C)=1/3+1/2-1/8=17/24
P(BUC)=0.71
