Flood insurance is determined by the federal government through the development of floodplains. One of the flood plains is called a 100 year flood plain, meaning the chance of experiencing a significant flooding event in a given year is 0.01. Assume that significant flooding events between years are independent.

(a) Find the probability the first significant flood will occur on or before year 100.

(b) Find the probability the second significant flood will occur on or before year 100.

(c) Find the probability the fourth significant flood will occur on or before year 100.

(d) Find the expected number of years with no significant flooding event before experiencing the third significant flood.

(e) Find the variance of the number of years with no significant flooding event before experiencing the third significant flood.