A box contains nine chocolates -- two with pecans, five with coconut, and two with raspberry creme. Harley Quinn eats three of the chocolates, chosen randomly. If it is known that at least one of the ones she eats has coconut, what's the probability that exactly two of them have coconut?
2. Beyoncé has seven background dancers for her performance at the Grammys, five of them are wearing black costumes and two are wearing white costumes. If two of the dancers are selected at random to join Beyoncé onstage for the encore, what is the probability that at least one will be wearing black given that at least one is wearing white?
3. A bag contains six 1-dollar bills, five 5-dollar bills, and two 10-dollar bills. An experiment consists of drawing three random bills from the bag simultaneously. Thus, the experiment has C(13,3)=286 equally likely outcomes in its sample space. What is the probability that at least two 5-dollar bills were drawn, given that no 10-dollar bills were drawn?
4. Suppose A={b,c,d,e}. A subset of A is selected at random -- i.e. all subsets have an equal chance of being selected. If the subset is not empty, what is the probability it contains the element b?
5. Paige Turner loves finite mathematics. She has six books about probability and five books about matrices. She lends her friend Anita Tudor four of these books, selected completely randomly. What is the probability Paige lends Anita two books on each topic (i.e. two matrix books and two probability books), given that she lends her at least one book on each topic? What is the probability Paige lends Anita four books on matrices, given that all the books she lends her are on the same topic?
6. A diplomatic team consists of eight Australians, including Dame Edna, and three New Zealanders, including Stephen Peter Kearney. The team must select two members to serve as officers: one as Spokesperson and another as Chairperson. The officers are selected at random. What is the probability that Dame Edna is the Chairperson given that Stephen Peter Kearney is the Spokesperson? What is the probability that Dame Edna is the Chairperson given that Stephen Peter Kearney is not the Spokesperson? What is the probability that both officers are New Zealanders given that they are both from the same country?
7. Two ordinary fair, six-sided dice are rolled. What is the probability the sum of the numbers on the two dice is 6, given that the number on at least one of the dice is 3? What is the probability the sum of the numbers on the two dice is 8, given that the number on at least one of the dice is 3? What is the probability the sum of the numbers on the two dice is 11, given that it is not 3? What is the probability exactly one of the dice shows the number 1 given that the sum of the numbers is 6?