Question

Gauss Club Spring 2019 FH 1-'9% Question 2. Suppose an influenza epidemic strikes a city. In t s of amu es the mother has m uenza, in 10% of anilies the father had influenza; and in 2% of families.both father have influenza. Furthermore, suppose there is a 20% chance.cach child whereas in 10% of two child familiesboth children.get the discase . Are A, and A2 independent Doyendent ooth varaet afe aleed by each o ndependant: bot variables haveno tooth eads oe Mo, has influenta ther las in thay are n b. What is the probability that at least one child will get influenza? FAD What is the probability that the father has influenza given that the mother has influenza? c.

Answer 1

a) here as P(A1 n A2)=0.02

while P(A1)*P(A2)=0.1*0.1 =0.01

as P(A1)*P(A2) is not equal to P(A1 n A2) ; therefore A 1 and A2 are not independent

b)

P(at least one child will get Influenza) =P(first child has)+P(2nd child has)-P(both child has)

=0.2+0.2-0.1 =0.30

c)

P(father has Influenza given mother has Influenza)=P(A2 |A1)=P(A1 n A2)/P(A1)=0.02/0.1 =0.20