A study was performed concerning medical emergencies on...

A study was performed concerning medical emergencies on commercial airline flights (Peterson, et al., [16] ). A database was constructed based on calls to a medical communications center from 5 domestic and international airlines representing approximately $10 \%$ of global passenger flight volume from January 1,2008 to October 31,2010 . There were 11,920 in-flight medical emergencies (IFM) among 7, 198,118 flights during the study period. Assume for this entire problem that there is at most 1 IFM per flight. Suppose a flight attendant works on 2 flights per day for each of 300 days per year. What is the probability that the flight attendant will encounter at least one IFM over a 1-year period?

A study was performed concerning medical emergencies on commercial airline flights (Peterson, et al., [16] ). A database was constructed based on calls to a medical communications center from 5 domestic and international airlines representing approximately $10 \%$ of global passenger flight volume from January 1,2008 to October 31,2010 . There were 11,920 in-flight medical emergencies (IFM) among 7, 198,118 flights during the study period. Assume for this entire problem that there is at most 1 IFM per flight.
Suppose a flight attendant works on 2 flights per day for each of 300 days per year. What is the probability that the flight attendant will encounter at least one IFM over a 1-year period?

Key Concepts

Complement Rule

The complement rule in probability is used to determine the likelihood that at least one event occurs by subtracting the probability that no events occur from one. This method simplifies calculation by focusing on the easier task of computing the probability of zero events across the individual flights and then subtracting that from one to find the probability of one or more events.

Binomial Distribution

The binomial distribution describes the number of successes in a fixed number of independent Bernoulli trials with the same probability of success. In this problem, the flight attendant’s 600 flights represent a series of Bernoulli trials, and the binomial distribution models the probability of encountering a given number of emergencies over these flights.

Bernoulli Trials

A Bernoulli trial is an experiment that has exactly two outcomes: success or failure. Each flight can be viewed as an independent trial with the probability of a flight encountering an in?flight medical emergency (success) and the probability that it does not (failure). This framework is central for modeling the problem when an event either happens or does not on each flight.

Rate Calculation

This concept pertains to determining the probability of an event from given frequencies. In the context of the problem, it involves computing the probability of an in?flight medical emergency by dividing the number of emergencies by the total number of flights. Understanding how to extract a rate from raw counts is fundamental in making subsequent probability calculations.

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