an advertising display contains a large number of light bulbs which are continually being switched on and off. Individual lights fail at random times, and each day the display is inspected and any failed lights are replaced. The number of lights that fail in any one day period has a poisson distribution with mean 2.2

a)what is the probability that no light will need to be replaced on a particular day?

b)what is the probability that at least 4 lights will need to be replaced over a stretch of 2 days ?

c)what is the least number of consecutive days after which the probability of at least one light having to be replaced exceeds 0.9999?