Math: Applications for Living — The Chance of That

Our Math-Applications for Living course is finishing up our work with statistics and probability.  A couple of students commented that they realized that their thinking had to change when we talked about probability — what seems natural for experts is not natural at all for novices.   This was an issue for combining probabilities — either a sequence (multiply) or options for one event (add).

On today’s test, one item seems to be really confusing:

Determine the probability of meeting someone whose phone number ends in the same digit as yours.

Students are asking “what about the rest of the digits” and “how many digits are we including for the phone number”.  From my point of view, this question was an attempt to measure the basic rule about probability — for random events, the probability is the ratio of “yes” to “total”.  We had dealt with this in other contexts, but I wanted something new on the test to see if they would apply the idea.

Probability continues to be one of the more challenging parts of the course.  One of the ironic results is that students appreciate the algebra that we will do next, because they seem to ‘get that’ a little better.

Of course, many of us who deal with probability do so within the context of a statistics course (as opposed to my survey-type course).  I wonder if you find that students have similar difficulties in ‘probabilistic thinking’.

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