Question

Facing an outbreak of shingles (chicken pox), the infected population can be partitioned into three age groups: above 80 years old (5% of population), 45 - 80 (55% of population), and below 45 years old (40% of population). We know that within the above 80 years old group 22% of them are not contagious; in the 45 - 80 group, 5% are not contagious; and below 45 years old the 0.6% are not contagious. What is the probability someone is under 45 years old, given they are not contagious? (It may help to draw a tree diagram.)

Answer 1

P(not contagious)=P(above 80)*P(not contagious|above 80)+P(45-80)*P(not contagious|45-80)+P(below 45)*P(not contagious|below 45)
	=0.05*0.22+0.55*0.05+0.4*0.006=0.0409

P(below 45|not contagious)=P(below 45)*P(not contagious|below 45)/P(not contagious)=0.4*0.006/0.0409=0.0587