Amy immigrated to a new city, and would like to make friends with her new neighbours.

On any particular day i, she feels shy with probability 1-p(0

(i) someone is at the house and answers the door; this happens with probability q (where 0

(ii) no one is at the house and Amy returns home.

We assume that the collection of all events of the form {Amy stays home on day i} and {Someone is at the i-th house on day i}, for i-1, 2,....., are (mutually) independent.

a.What is the probability that Amy gives out a picture on the first day?

b.Fix some integers k and n, with n>= 1 and 0 <=k<=n. What is the probability that she gave out exactly k pictures on the first n days?

c.What is the probability that she stayed home on day 1, given that she did not give out a picture on that day?

d.Within the first week (7 days), what is the probability that there were no days in which Amy went out but did not give out a picture of her hometown?