Probability Problem

The Mathematical Olympiad Handbook: An Introduction to Problem Solving Based on the First 32 British Mathematical Olympiads 1965-1996 (Oxford Science Publications)

1. A survey of the non-healthy habits of 80 sophomore students of a certain seminary showed the following result.
45 drink alcoholic beverages
42 stay up late
40 smoke cigarettes
25 drink alcohol and smoke
19 stay up late and smoke
22 drink alcohol and stay up late
9 practice clean healthy living by not doing any of the 3

If a seminarian sophomore is randomly picked, what is the probability that he:
a. is just an insomniac (or just stay up late)
b. smokes and/or drinks but is a sleepyhead (or smokes and/or drinks but sleeps early)
c. he should be kicked out of the seminary (by doing all the three things)


2. What is the probability that a path from (0,0) to (8,6) pass through (5,4), assuming that all paths move along grid lines and that movement must be either the positive x or the positive y direction?