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.

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