A tall building is designed for a 100-year wind; i.e. the probability of annual maximum wind speed exceeding the design speed is 1%.
a) What is the probability that the design wind speed will be exceeded for the first time on the fifth year after completion of the building? How about the probability of it on the tenth year?
b) What is the probability that the first such wind occur within 5 yrs after completion of the structure? How about the probability of it within 10 yrs?

Kindly show formulas in solution. Thanks.

P(building falls down in a given year) = 0.01
P(building doesn't fall down in a given year = 1-P(fall) = 0.99

a) That's four years in a row not falling down plus one year of falling down:
P(no fall)^4 * P(fall)
Or, the second part, is nine years not falling down plus one year falling down:
P(no fall)^10) * P(fall)

b) Within five years means 1 minus not within five years:
1-P(no fall)^5
Or, one minus not within ten years:
1-P(no fall)^10