Suppose an airport metal detector catches a person with metal 99% of the time. That is, it misses detecting a person with metal 1% of the time. Assume independence of people carrying metal. What is the probability that the first metal-carrying person missed (not detected) is among the first 50 metal-carrying persons scanned?
Step 1 of 2:
Given that an airport metal detector 99% of the time catches a person with metal and fails to detect at 1% of time.
We have to calculate the probability that first person carrying metal is not detected or missed to detect is among the first 50 persons carrying metal.