A civil engineer examining the deformation of a bridge structure over time. He installed 20 sensors at different locations to record the required data. Assume that each installed sensor will operate
for more than 3 months with a probability of 20 %.

(a) Estimate the probability that at most 5 of the sensors will operate more than 3 months.

(b) After 3 months, what is the average number of sensors that have to be replaced (failed
sensors) in order to avoid any interruption in the data collection?​