Manufacturing and Product Development
A company has developed a very inexpensive explosive-detection machine for use at airports. However, if an explosive is actually in a suitcase, the probability of it being detected by this machine is only 0.60. Therefore, several of these machines will be used simultaneously to screen each piece of luggage independently. Suppose a piece of luggage actually contains an explosive.
a. If three machines screen this luggage, what is the probability that exactly one will detect the explosive? What is the probability that none of the three will detect the explosive?
b. If four machines screen this luggage, what is the probability that at least one device will detect the explosive?
c. If five machines screen this luggage, what is the probability that at least one device will detect the explosive?
d. How many machines are necessary for screening in order to be certain that at least one device will detect the explosive with probability 0.999 or greater?