Question

The article "Anxiety Increases for Airline Passengers After Plane Crash" (San Luis Obispo Tribune, November 13,2001 ) reported that air passengers have a 1 in 11 million chance of dying in an airplane crash. This probability was then interpreted as "You could fly every day for 26,000 years before your number was up." Comment on why this probability interprctation is mislcading.

Short answer

The interpretation 'You could fly every day for 26,000 years before your number was up' is misleading as it implies a certainty of an event (crash) after a specific time period, misunderstanding that with each flight, the probability of crash remains constant (1 in 11 million) regardless of the frequency of flights since each flight is an independent event.

Step-by-step solution

Understanding the Probability and its Interpretation

To begin with, we have a given probability of dying in an airplane crash as 1 in 11 million. This probability was interpreted in a way which suggests that if a person started flying everyday, it would take 26,000 years for them to experience a plane crash. In reality, each flight is a separate and independent event - meaning the probability doesn't decrease or increase based on the frequency of flights.

Concept of Independent Events in Probability

In statistics, two events are independent if the occurrence of one does not affect the occurrence of the other. In this scenario, each flight taken by a person is an independent event. Therefore, whether a person flies once or a thousand times, the probability of a crash is the same - 1 in 11 million.

Explaining the Misleading Interpretation

The statement 'You could fly every day for 26,000 years before your number was up' is misleading because it implies that there is a certainty that a crash will happen after 26,000 years of daily flights, which is not true. This is a lapse in understanding the fundamental nature of probabilities - they do not guarantee any outcomes, but merely provide a statistical likelihood.