At the Statistics Department Annual Party, there is a graduate student raffle for 7 prizes. Each graduate student is provided one ticket. There 85 tickets distributed to all of the graduate students. Tallis is a new student and really wants to win. He asks his friends to give him their tickets. Tallis ends up with 4 tickets total. Each of these tickets will either win a prize or not win a prize. (note: think about the sample size.)

a) The announcer reveals the winning tickets. Let W be the number of winning tickets Tallis has. What is the probability he wins at least one prize. What is the distribution, parameter(s), and support of W?

b) What is the expected number of prizes Tallis expects to win?

c) Given that Tallis wins at least one prize, what is the probability he wins two or three?

d) Is there a way to approximate the probability regarding Tallis winning any prizes? If so, state the distribution, parameter(s) and support, along with the reason that the approximation is valid.

e) Using the approximation, what is the probability Tallis wins at least one prize?