On average 34 % of Finite Mathematics students don't spend any time in the Mathematics Department's resource room (event R11), 33 % of the students spend between 1 and 90 minutes in the resource room (event R22) and 33 % of the students more than 90 minutes per week in the resource room (event R33). At the end of the semester the students in the class were asked how many minutes per week they spent in the resource room and whether they passed or failed. The passing rates are summarized in the following table:

Time spent in resource room	Pass %
None	29
Between 1 and 90 minutes	52
More than 90 minutes	73

If a randomly chosen student did pass the course, what is the probability that: a) He or she did not study in the resource room? P(did not study | pass)=(did not study | pass)= b) He or she studied between 1 and 90 minutes in the resource room? P(studied 1 to 90 | pass)=(studied 1 to 90 | pass)= c) He or she studied more than 90 minutes in the resource room? P(studied > 90 | pass)=(studied > 90 | pass)=: Hint: If we denote by Q the event that a student passes the course the above table gives P(Q|Ri)(|) for i = 1, 2, 3 and P(Ri)() are given in the text. You are asked for P(Ri|Q)