b. Calculate the probability of the mother having the flu, given that the father

Question

b. Calculate the probability of the mother having the flu, given that the father already has the flu

c. What is the probability that at least one parent has the flu?

A flu epidemic has struck the city. In 10% of the families, the mother has the flu. In 20% of the families the father has the flu. In 4% of the families both parents have the flu. Consider the following events for contracting influenza in a household of four: M-mother has flu F father has flu 1st first child has flu 2nd- second child has flu

Explanation / Answer

Solution:

a) The probabilities of 1st and 2nd are non-disjoint is a True statment. because occurance of first does not depend on occurance of the second.

b) probability of the mother having the flu, given that the father already has the flu
= P(M|F) = P(M F) / P(F)
= 0.04 / 0.20 = 0.20

c) probability of at least one parent having the flu = 0.10 + 0.20 -0.04 = 0.26

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