[2 points each, Total 10 points] a. An octahedral die has eight faces. One octahedral and one regular die with six faces are rolled together. What is the probability of getting the sum of number 10? A player in the Mega Millions lottery picks five different integers between 1 and 56, inclusive, and a sixth integer between 1 and 46, which may duplicate one of the earlier five integers. The player wins the jackpot if the first five numbers picked match the first five numbers drawn, and the sixth number matches the sixth number drawn. What is the probability that a player wins the jackpot? Suppose that p and q are primes and n = pq. What is the probability that a randomly chosen positive integer less than n is not divisible by either p or q? A card player pulls 13 cards out of a deck. What is the probability that he gets seven cards of hearts and 6 cards of spades? Suppose that A and B are events with probabilities p(A) = 3/4 and p(B) = 1/3. What is the largest p(A n B) can be? Explain. (Hint: Use Venn diagram)