The Binomial Distribution and Test, Clearly Explained!!!

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3:00Under equal preference and independent responses, a specified Orange–Orange–Grape sequence has probability ($1/2$)³=$1/8$. Exactly two Orange preferences also includes the other orderings.

4:30There are three positions for the Grape response, so exactly two Orange responses among three has probability $3/8$. The combination coefficient packages this counting into the binomial formula.

13:30For four Orange responses out of seven under $p=1/2$, the lesson’s two-sided probability-ordering test gives p-value one. This does not establish equal preference; it means the sample does not provide evidence against that null under this test.

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