Can we calculate probabilities without assuming independence?

[phospho]

The probability that john will go to UCLU is estimated at 1/5; the probability that he will go to some other university is 1/3. The probability that his sister Mary will go to UCLU is 1/4. Calculate the probabilities that:

a) John and Mary both go to UCLU;
b) John will not go to university;
c) either John or Mary but not both will go to UCLU

Is it possible to do a) without assuming that they are independent events? Are we allowed to just assume that events are independent? In real life John going to university surely is not independent of his sister going university. E.g. if John goes UCLU then his sister, may be more motivated to study harder and thus go into UCLU...?

Also, if two events are not independent, does it mean they are dependent?

 

[haruspex]

You are correct: to solve the problem you need to assume the events are independent, though in real life they may not be. Yes, if they're not independent then they are in some way dependent.

 

[Ray Vickson]

The probability that john will go to UCLU is estimated at 1/5; the probability that he will go to some other university is 1/3. The probability that his sister Mary will go to UCLU is 1/4. Calculate the probabilities that:

a) John and Mary both go to UCLU;
b) John will not go to university;
c) either John or Mary but not both will go to UCLU

Is it possible to do a) without assuming that they are independent events? Are we allowed to just assume that events are independent? In real life John going to university surely is not independent of his sister going university. E.g. if John goes UCLU then his sister, may be more motivated to study harder and thus go into UCLU...?

Also, if two events are not independent, does it mean they are dependent?

Just to clarify: the two events involving John alone are mutually exclusive (unless John can attend two universities at the same time). Mutual exclusiveness is about as dependent as you can get.