3 Erika is a birdwatcher. The probability that she will see a woodpecker on any given day is \(\frac { 1 } { 8 }\). It is assumed that this probability is unaffected by whether she has seen a woodpecker on any other day.
- Calculate the probability that Erika first sees a woodpecker
(a) on the third day,
(b) after the third day. - Find the expectation of the number of days up to and including the first day on which she sees a woodpecker.
- Calculate the probability that she sees a woodpecker on exactly 2 days in the first 15 days.