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Does anyone understand their argument clearly?

For three flips I get this sample space:

TTT no data; TTH no data; THT one data point HT; THH one data point HH; HTT one data point HT; HTH one data point HT; HHT two data points HH, HT; HHH two data points HH, HH

total data points by result: HT 4 HH 4

For four flips it's the same deal, after an H I'm equally likely to get another H or a T. Of course.

What am I missing? I don't quite understand their definition of 'empirical probability.'




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