Question: An area of a computer laboratory housing temperature sensitive equipment has temperature sensors installed which give an alarm when the temperature rises above a certain level. Individual sensors have only a 95% chance of giving a warning when the danger level is reached. Consequently, several sensors are fitted and they all function independently. If 3 devices are fitted, what is the probability that:

a). exactly 2 function correctly,

b). at least 2 function correctly?

How many should be fitted to ensure at least a 99.99% chance of getting a warning signal when necessary?