probabilities

Question

The probabilities that John will choose Physics, Chemistry and Biology in the summer semester are 0.4, 0.7 and 0.6, respectively. If John has decided to choose Physics, the probabilities of choosing Chemistry and Biology are increased to 0.8 and 0.75, respectively. On the other hand, if he has decided not to choose Biology, the probability of choosing Physics only becomes 0.05. The probability that John will choose both Chemistry and Biology but not Physics is 0.15.

a) What is the probability that John will choose Physics only?

(b) What is the probability that John will choose all three courses?

(c) What is the probability that John will not choose any course in the summer semester?

Answer 1

Ka,

You can write this in a formal conditional logic manner, but it's far more intuitive to map it as a Venn diagram, maybe redrawing it a few times as you gradually incorporate the various conditional probabilities. So, for example, within the Physics circle (at 0.4 of total probability = 1), an overlap with chemistry has p(C|P)=0.8. So P.intersect.C is 0.4*0.8 = 0.32 (absolute); P.intersect.B = 0.4*0.75 = 0.3 (absolute) , and so on until you have all the diagram areas accounted for. Then it's easy to pick the data to answer the 3 questions.