A city has calculated the probability of having a significant rupture in a year: p = 0.08. This probability remains fixed from year to year, independent of whether there was a rupture in a preceding year. The city has asked you to determine the following (for each question be sure to specify what probability model you are using being sure to justify your choice.)

(a) The probability that the first rupture will occur in the 7th year.

(b) The expected number of years until the first rupture.

(c) The probability of exactly 7 ruptures in the next 17 years

(d)The standard deviation, of the number of ruptures in the next 17 years.

(e)The probability that the first rupture occurs in one of the first 7 years.