2 A group of friends live by the sea. Each day they look out to sea in the hope of seeing a dolphin. The probability that they see a dolphin on any day is 0.15 . You should assume that this probability is not affected by whether or not they see a dolphin on any other day.

1. Explain why you can use a geometric distribution to model the number of days that it takes for them to first see a dolphin.
2. Find the probability that they see a dolphin for the first time on the fifth day.
3. Find the probability that they do not see a dolphin for at least 10 days.
4. Determine the mean and the variance of the number of days that it takes for them to see a dolphin.