Two diseases A and B have spread within a certain population. We

know that 15% of this population have the disease A, 20% of this

population have disease B and 25% have at least one of the two diseases.

We choose a random person among this population.

(a) What is the probability that this person contracted both diseases?

(b) Given that the chosen individual has at least one of the diseases,

what is the probability that this person has contracted both dis-

eases?