[Statistics] Confused about probability
During the orientation week, a certain movie was shown twice at a certain University. Among the entering class of 2000 freshmen, 850 went to see it the first time, 690 the second time, while 730 failed to see it either time. If I pick a freshman at random, what is the probability that that freshman has seen the movie twice?
At first I thought it was just the inclusion-exclusion principle, but it's clearly not. So I know that at most, 690 people can have seen the movie twice, but I don't know how to narrow it down further.
Posted Oct 6, 2016, 8:33 PM UTC
12
730 failed to see the movie, so 2000-730=1270 did see it (either once or twice). Of the 1270 who saw it, 850 were present at the first showing, so 1270-850=420 must have attended only the second showing. Since a total of 690 attended the second showing, 690-420=270 must have attended both shows. 850-270=580 is the number of students who attended only the first show.
Oooo. I understand now. Thanks!