The designer of a highrise building is interested in perform

The designer of a high-rise building is interested in performance of the structure when subjected to wind speeds grater than 40 miles per hour (mph).A review of the wither record for the last 3 to 4 decades indicated that there is 20% probability of wind speeds exceeding 40 mph in any one year. Assume wind speed from one year to another are statistically independent. Calculate the following. probability that winds exceeding 40 mph will occur consecutively for 4 years probability that winds less than 40 mph will occur consecutively for 4 years.

Solution

P(Speed > 40 mph) = 0.20

So,

a. P(Speed > 40 mph for 4 independent years) = 0.20⁴ = 0.0016

b. P(Speed < 40 mph for 4 independent years) = (1 - 0.20)⁴ = 0.4096

c. P(Speed > 40 mph for 1st time in 4th year) =

P(Speed < 40 mph for 3 independent years) * P(Speed > 40 mph for 4th year) = (1-0.20)³ * 0.20 = 0.1024