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# Suppose an airport metal detector catches a person with

ISBN: 9780321923271 41

## Solution for problem 4E Chapter 2.5

Probability and Statistical Inference | 9th Edition

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Problem 4E

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-by-Step Solution:

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.

Step 2 of 2

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