Question

Q7. A company has developed an explosive-detection machine for use at airports. If an explosive is in a suitcase, the probability of it being detected by this machine is 0.6. Several of these machines will be used simultaneously to independently screen each piece of luggage. Suppose a piece of luggage actually contains an explosive.

1. (4pts) If three machines screen this luggage, what is the probability that exactly one detects the explosive? What is the probability none of the three detects the explosive?

2. (4pts) If four machines screen this luggage, what is the probability that at least one device detects the explosive?

3. (4pts) How many machines are necessary for screening in order to be certain that at least one device defects the explosive with probability 0.999 or greater?

Answer 1