Imagine you asked three people about their preference between apples and oranges. What would be your conclusion if the first two preferred apples and the third liked orange? Does it mean more people like Apple, or did it happen by random chance?
One way to deal with it is to test and get the probability of the hypothesis that people have no preference. So, let’s analyse what happened.
No preferred assumption means the probability of a person saying apple or orange is 0.5. The probability of the first two persons randomly choosing an apple and the third person randomly choosing an orange is,
0.5 x 0.5 x 0.5 = 0.125
But this is not what we are after. The situation can as well be the following,
or
The probability of situation 1 OR situation 2 OR situation 3 = sum of the three probabilities. It is 0.125 + 0.125 + 0.125 = 0.375.
Binomial distribution
It is the same thing we have seen in binomial probability distribution. The probability of s successes in n rounds is
nCs x ps x q(n-s)
