How to know when to use which probability distribution?

57% of students studied, which decomposes into  52% who both studied and saw an increase in their exam grade  5% who both studied and did Not see an increase in their exam grade The percentages above are relative to the whole population of 100 students, to get the requested probability, recall that:   One way to find out the probability of an event is to  Take the ratio of the number of times the event happened, over the total number of times the event could have happened.    Total number of times the event happened:    52 = 52% of 100 students studied and saw an increase in their exam grade  Total number of times the event could have happened:    57 = 57% of 100 students studied