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Chapter 4: Problem 21

Suppose a randomly selected passenger is about to go through the metal detector at JFK Airport in New York City. Consider the following two outcomes: The passenger sets off the metal detector, and the passenger does not set off the metal detector. Are these two outcomes equally likely? Explain why or why not. If you are to find the probability of these two outcomes, would you use the classical approach or the relative frequency approach? Explain why

Short Answer

Expert verified
No, the two outcomes are not equally likely. The relative frequency approach would be the appropriate method to calculate their probabilities due to the variables and real world conditions involved.

Step by step solution

01

Understanding the situation

First, one must make clear that whether a passenger sets off a metal detector at the airport is based on numerous variables. These could be - if they have any metal objects on or inside them, how sensitive the detector is, etc. It is not a purely random situation where all outcomes are equally likely.
02

Likelihood of outcomes

Given that not every passenger will carry metal items, it's logical to conclude that the 'not setting off the detector' event should be more probable. In other words, the two outcomes are not equally likely.
03

Approach to calculate probabilities

To determine the probabilities of these outcomes, the relative frequency approach would be more appropriate than the classical approach. Given real world conditions and variations, it would be more accurate to collect a large sample of observed outcomes (number of times the detector was set off versus not set off) and calculate the relative frequencies (probabilities).

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