Question

1. A physician at a large clinic sees clients of all ages: babies (<2 years old, event B), children (2-18 years old, event C), and adults (>18 years old, event A). Let N denote the event that the next client she sees is a new patient. Suppose that P(N) = 0.23, P(C) = 0.41, P(N∩C) = 0.10, P(B|N) = 0.043, P(B|N’) = 0.026.

a. Find the probability that a patient is a new patient given that the patient is a baby.

b.Find the probability that the patient is a baby.

c.Find the probability that the patient is an adult and a new patient.

d. Are the events N and C independent? Explain.

Answer 1

a)

P(N|B) =P(N)*P(B|N) /(P(N)*P(B|N)+P(N')*P(B|N') =(0.23*0.043)/(0.23*0.043+0.77*0.026)

=0.3307

b)

P(B) =(P(N)*P(B|N)+P(N')*P(B|N') =0.23*0.043+0.77*0.026 =0.0299

c)

P(A n N) =P(N)-P(N n C)-P(N n B) =P(N)-P(N n C)-P(N)*P(B|N) =0.23-0.10-0.23*0.043 =0.1201

d)

since P(N)*P(C) =0.23*0.41 =0.0943 is not equal to P(N n C) , event N and C are not independent,