Answer:
0.395 or 39.5% probability that the first metal-carrying person missed (not detected) is a
Step-by-step explanation:
The easiest way to solve this problem is to determine the probability of all 50 of the first 50 metal-carrying people scanned being caught by the metal detector (P(C)). Then, the probability that the first metal-carrying person missed is within the first 50 (P(M)) is 100% minus the probability of all 50 being caught:
[tex]P(C) = 0.99^{50}\\P(C) = 0.605[/tex]
[tex]P(M) = 1- P(C) \\P(M)= 1- 0.605\\P(M)=0.395[/tex]
There is a 0.395 or 39.5% probability that the first metal-carrying person missed (not detected) is among the first 50 metal-carrying people scanned.
