Question

I think this review problem involves Bayes Theorem but was stuck on how to approach it. Could you please guide me on how to approach this type of problem? Thank you!

Many cities are connected along the Nile River. Cities such as Aswan, Juba, and Jinja lie along the river as you move down the river. The annual probabilities of flooding are .2, .3, and .1 for the towns Aswan, Juba, Jinja respectively. The events of flooding in the cities Aswan, Juba, Jinja are not statistically independent. If Aswan is flooded in a given year, the probability that Juba will be flooded in the same year is increased to .6; if Aswan and Juba are flooded in a given year, the probability that Jinja will be flooded is increased to .8. However, if Aswan does not experience any flooding in a given year, then the probability that both Juba and Jinja will also not suffer any flooding in that year is .9. In a given year, if all three cities are flooded, it is regarded as a “disaster” year. Suppose the flooding events between any two years are independent.

(a) What is the probability that a given year is a disaster year?

(b) If Juba is flooded in a given year, what is the probability that Aswan is also flooded?

(c) What is the probability that at least one city is flooded in a given year?

Answer 1