I am not an expert at probability, So I would really like to see other replies
#1 If I flip a coin three times what is the probability of ATLEAST one head. Well, I can get one, two or three heads. In this case I think it would be easier to calculate the probablity of no heads. Then 1-P(no Heads) would be P(atleast one Head).
#2 If I remember right Disjoint means that they have nothing in common. If 840 went to the atheletic banquet and 460 went to the Winter formal then there are 100 students that went to both.
840+460 = 1300 but there are only 1200 students, so 100 went to both events
#3 (I might be wrong) If she is only guessing I think it is still 50/50. You see she doesnt know which are true and which are false. They could all be true and she might think that atleast 2 are false, but the point is she doesnt know which is true or which is false. I think the probability is 1/2^5
More Input On This One Would Be Nice