Probability, Decision Making, The Planet, and You

Rain Tomorrow in India

Now we'll explore the concept of relative frequency with the example of a weather forecast for Rain Tomorrow in India. Just like the example of Lefthanders in Argentina, this problem also relies on a numerical probability estimate (such as 11%). To have a probability estimate, two ingredients are required:

1. a careful definition of the uncertain event, so that we can know when it has actually occurred and when it has not. In this case it will be the equivilent of measuring rain in a bucket-like device.

2. a systematic method of recording and analyzing events of that same type that has proven correct in past experience. In this case it will be agreed upon scienfitic methodology of estimating the probability of rain based on the historical record of rain.

With the present example of Rain Tomorrow in India, you will see a definition of the uncertain event, how such an event is measured, and some discussion of how of events of the same type have been recorded and analyzed systematically.

Let's begin with the first ingredient, a careful definition of the uncertain event. For example, when a meteorologist states that there is a 70% chance of rain tomorrow in India, the event is usually defined by a threshold rain-gauge measurement at a definite weather station. Let's call it Weather Station A and the measurement device at this station is pictured. Here at Weather Station A, "rain" might mean a measurement of at least 1 mm of rainwater accumulating during a specific 24-hour period. That is the amount of rain that needs to fall in the collection device in order to meet the definition of having had "rain". This is how a careful definition of an uncertain event is constructed--to have "rain", we must meet these conditions.

Now let's look at the second ingredient, a systematic method of recording and analyzing events in ways that have proven correct in past experience. The method for estimating probability of rain in India is just like the rest of the world in that it involves calculations (or models) that have been shown to be accurate in the past history of attempting to predict when it will, in fact, rain. Specifically, looking at the historical record where the scientist's calculation has led to an estimate of rain in India in conditions similiar to today's, the event of rain has actually been observed in about 70 out of every 100 occasions. Thus, if the calculations (or models) are predicting rain tomorrow based on conditions that have in the past have yeilded actual rain in 70 of the past 100 occasions, then the same estimate of 70% chance of rain is offered. Again, since they have been right 70 of 100 times in the past with the same conditions present, the prediction of a 70% chance of rain tomorrow is made.

As an illustration, if we surveyed 200 occasions on which there has been a prediction of 70% probability of rain in India, from different times and places around India, we would expect that the actual weather meets the stated definition of "rain" about 140 times. (This is analogous to finding about 22 left-handers in a survey of 200 people, which confirms a probability estimate of 11%.)

Exercises

 

Exercise 1

1. Suppose you listen to the weather report every morning to hear what the chances are that it will rain during the day. Over a particular season, there were 50 times that the weather announcer said there was a 30% chance of rain. Of those 50 days, it actually rained on 15 days. Is this what you would expect?

 

 

Exercise 2

Suppose that there are 200 different towns and villages around the world that each have a 70% probability of rain estimated for tomorrow. In how many should we expect NO rain (that is, less than 5mm in 24 hours)


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