Match each description with its symbolic representation. 1. p (a) the probability that both events a and b do not occur together, but either may occur by itself 2. p (a ∩ b) the probability that event a occurs 3. p (a ∪ b) the probability that neither event a or event b occurs 4. 1 - p (a ∩ b) the probability that event a occurs given the fact that event b occurs 5. 1 - p (a ∪ b) the probability that either event a or event b occurs 6. p (a | b) the probability that both event a and event b occur

Exercise: counting committees 0.0/2.0 puntos (calificable) we start with a pool of n people. a chaired committee consists of k≥1 members, out of whom one member is designated as the chairperson. the expression k(nk) can be interpreted as the number of possible chaired committees with k members. this is because we have (nk) choices for the k members, and once the members are chosen, there are then k choices for the chairperson. thus, c=∑k=1nk(nk) is the total number of possible chaired committees of any size. find the value of c (as a function of n ) by thinking about a different way of forming a chaired committee: first choose the chairperson, then choose the other members of the committee. the answer is of the form c=(α+nβ)2γn+δ. what are the values of α , β , γ , and δ ?