There are 7 strangers in a room. Let E7E7 denote the event that no two of them celebrate their birthday in the same month. Assume that all possible monthly outcomes are equally likely.

P(E7)P(E7) =

a) Roll a fair six-sided die until an odd number comes up. What is the probability that the number of rolls required is 13? b) Roll a fair six-sided die until a 4 comes up. What is the probability that the number of rolls required is 13?

An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 100 students in the school. There are 23 students in the Spanish class, 24 in the French class, and 13 in the German class. There are 10 in both Spanish and French, 8 in both Spanish and German, and 4 that are in both French and German. There are 3 students taking all 3 classes.

(a) If a student is chosen randomly, what is the probability that he or she is not in any of these classes?

(b) If a student is chosen randomly, what is the probability that he or she is in exactly one of these classes?

(c) If a pair of students are chosen randomly from the 100 students, what is the probability that at least 1 is taking a language class?