(Solved): Professors at Istanbul Medipol University either have ARDEB (A), TUBITAK (T) or BAP (B) projects. T ...

Professors at Istanbul Medipol University either have ARDEB (A), TUBITAK (T) or BAP (B) projects. The probability of professors having ARDEB is 0.30, while the probability of those having TUBITAK is 0.20. On the other hand, it is known that 40% of the professors are foreign nationals (F). It is also given that 40% of the foreigners own BAP , while 30% of them own ARDEB project. As for the Turkish nationals or locals (L), 20% of them have ARDEBand 50% of them have TUBITAK. a) (5 pts.) Draw the Venn Diagram and label all the events with their associated probabilities. b) (5 pts.) What is the probability of a professor being Turkish given that he/she has got a BAP project? c) (5 pts.) What is the probability of a professor being foreigner and owning a TUBITAK project? d) e) (5 pts.) What is the probability that the professor is foreigner knowing that he/she does not own an ARDEB project? (5 pts.) Show mathematically and intuitively if the events of being a foreign professor and having an ARDEB project independent or not.