Question

A customer purchases a lottery ticket that requires him to select six numbers. A few minutes later, another customer purchases a ticket, also choosing six numbers.

Are these two events dependent or independent?

Answer 1

Independent. One customer's choice does not change the probability of what the other customer will choose (unless the lottery forbids duplicate selections). By the usual definition, events A and B are independent if P(B) is unchanged by knowing A; here the second pick's probabilities are unaffected by the first pick, so they are independent.