Thinking about starting probability today – in fact it’s in the syllabus.  Am I moving too quickly?

Finding the probability that a state’s name begins with ‘M’ is easy. Finding the probability that a random word in English begins with ‘M’ is harder. The class went immediately to google and then wandered around on the web. What I hoped for never happened – just thinking. I suggested the number of ‘M’ pages divided by the number of pages in the dictionary – but no one uses dictionaries these days. Then I talked about how the sample space matters – a random word in today’s paper isn’t the same as a random word in a dictionary.

Sample space was the issue too in this problem from the book:

The average citizen visits a coastal shore, Great Lake, or river about 10 days
a year, according to a federal estimate . . .
About 3.5 million people each year get sick enough to be nauseated or get
diarrhea after splashing in water containing harmful bacteria, according to an
Environmental Protection Agency estimate.

To estimate the probability of illness from a visit to the beach you need

(3.5 million)/(total visits) = (3.5 million)/(10 * population)

which just over a tenth of a percent: one chance in a thousand. But almost no one realized that was the denominator you wanted.

I need to make this clearer in the text.

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