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Mutually Exclusive Events

Probability of two events that cannot occur at the same time P(A or B) = P(A) + P(B)

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When to Take Cover

Credit: Pato Garza
Source: http://www.flickr.com/photos/pato_garza/7539199336/
License: CC BY-NC 3.0

Each year more than 100 people die in the United States due to storm-related fatalities (tornadoes, wind, hail, and lightning). The Storm Prediction Center (SPC) in Norman, Oklahoma is responsible for issuing watches and warnings during storms so that people located in a storm’s path can seek shelter before it’s too late.

Why It Matters

The SPC tracks many different weather-related events and uses probabilities to determine the threat of each storm. In particular, the SPC looks for threats of high winds, hail, and tornadoes in order to make predictions about severe weather. If the prediction is that just one of those three events will occur or the probability that those events will occur is less than 30%, then the SPC issues a “Slight Risk Watch” that isolated weather events will occur. If there is a greater probability (45%) of widespread hail, moderate winds, and/or numerous tornadoes, then the SPC will issue a “Moderate Risk Watch.” A “High Risk Watch” is issued when there exists a high probability (60%) that there will be strong tornado outbreaks, destructive winds, and large hail. High risk days are quite rare, and when a high risk is determined for an area, residents are often encouraged to take shelter.

Credit: FEMA
Source: http://commons.wikimedia.org/wiki/File:FEMA_-_44968_-_Tornado_in_the_late_evening_sky.jpg
License: CC BY-NC 3.0

The SPC assesses not just the likelihood of any single event occurring (high wind, large hail, or tornadoes) but also the likelihood that they will happen together. When a storm is determined to be high risk, it is because multiple events are occurring simultaneouslythose events are not mutually exclusive.

See for yourself: http://www.oar.noaa.gov/k12/html/forecasting2.html

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  1. Are the events of hail and high wind mutually exclusive? Why or why not?
  2. If there is a “High Risk Watch” issued for a particular storm, what overlapping events will likely occur?

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