Math: Applications for Living XVIII “At Least Once”

As you ‘probably’ know, probability reasoning does not come easily for many students. In our Applications for Living course, we cover some basic probability ideas and situations where they apply. We have been struggling through a type called ‘at least once’.

Here is an example:

The probability that a particular region in Mexico will be hit by a hurricane in any given year is 0.1. Find the probability that the region will be hit by a hurricane at least once in a 10 year period.

Students have a tendency to multiply the probability by the value of n, even though we have already discovered that this is not a correct method of a sequence of events. We do work with a formula that our textbook provides: P(at least once) = 1 – P(not)^n. However, progress has only been made by taking this in three steps.

If the probability of it happening is 0.1, then the probability of it not happening is 0.9 (1 – 0.1)
At least once means all sequences except “not at all” in the 10 years.
The probability of “not at all” in 10 years is 0.9^10 (about .3487)
1 – 0.3487 = 0.6513 (the probability of at least once in 10 years)

Students in my class live in Michigan (this is a face-to-face class), so hurricanes are not an event we need to plan for. However, we use the same approach for floods and tornadoes, which do occur here.

Our course is finishing up our work with statistics and probability. Students have discovered that these topics are more about reasoning than about calculating, which is not always a pleasant discovery. Our hope, of course, is that reasoning in one domain (probability) transfers to other domains (in mathematics, and outside as well).

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