Question: 1 . Consider a simple lottery where we randomly draw k balls from some balls numbered from 1 to n. If the prize for winning

1 . Consider a simple lottery where we randomly draw k balls from some balls numbered from 1 to n. If the prize for winning is the same for each, which is a better option for players?

Lottery 1: k = 4, n = 50

Lottery 2: k = 3, n = 40

2 . Suppose we have an e-mail spam filter. If a message is spam, it has a 99% chance of blocking it. If a message is not spam, it still has a 5% chance to block it. Assume 2% of e-mails received are spam. If the filter blocks a message, what is the probability that it was actually spam?

3 . Use the PGF g(z)=(1p+pz)3 to determine the corresponding PMF and then state which distribution it has and state the parameters.

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