In Michigan’s Classic Lotto 47 Lottery, a player must choose six numbers between 1 and 47, inclusive. Six balls numbered from 1 to 47 are then randomly selected from an urn. The random variable X represents the number of matching numbers. What is the probability of matching,

(a) 3 numbers?

(b) 4 numbers?

(c) 5 numbers?

(d) 6 numbers?

(e) A winning ticket is one in which the player matches 3, 4, 5, or 6 numbers. What is the probability of purchasing a winning ticket? Would it be unusual to purchase a winning ticket?

(f) What is the mean and standard deviation of the random variable X? For a randomly selected ticket, how many numbers do you expect to match?