A dental insurance policy covers three procedures: orthodontics, filling, and extractions. During the life of the policy, the probability that the policyholder needs: Orthodontic work is 1/2 Orthodontic work or a filling is 2/3 Orthodontic work or an extraction is 3/4 A filling and an extraction is 1/8 The need for orthodontic work is independent of the need for a filling and is independent of the need for an extraction. Calculate the probability that the policyholder will need a filling or an extraction during the life of the policy.

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RIVERBuenosAires RIVERBuenosAires · Answer 1 · 2019-09-25T00:21:37+02:00

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