(Solved): 1. A hat contains six slips of paper with the numbers 1 through 6 written on them. Two slips of pa ...

1. A hat contains six slips of paper with the numbers 1 through 6 written on them. Two slips of paper are drawn from the hat (without replacing), and the sum of the numbers is computed. (a) What is the probability that the sum of the numbers is exactly 10 ? (b) What is the probability that the sum of the numbers is at least 10 ? (c) What is the probability that the sum of the numbers is exactly 10, given that it is at least 10 ? 2. Suppose you do an experiment where you select ten people at random and ask their birthdays. Here are three events: $$A$$ : all ten people were born in February. $$B$$ : the first person was born in February. $$C$$ : the second person was born in January. (a) Which pair(s) of these events are independent, if any? (b) What is $$P(B?A)$$ ?