Page "Binomial test" Paragraph 5

To find an answer to this question using the binomial test, we consult the binomial distribution B ( 235, 1 / 6 ) to determine the probability of finding exactly 51 sixes in a sample of 235 if the true probability of rolling a 6 on each trial is 1 / 6.

We then find the probability of finding exactly 52, exactly 53, and so on up to 235, and add all these probabilities together.

In this way, we calculate the probability of obtaining the observed result ( 51 6s ) or a more extreme result (> 51 6s ) assuming that the die is fair.

In this example, the result is 0. 0265443, which indicates that observing 51 6s is unlikely ( significant at the 5 % level ) to come from a die that is not loaded to give many 6s ( one-tailed test ).