 Solution

Use the Pearson chi-squared goodness-of-fit test. Under the null hypothesis, each count has the specified binomial distribution, and no parameter is estimated from the data. The seven mutually exclusive classes give $7-1=6$ degrees of freedom. Their expected counts are all at least five, so the usual chi-squared asymptotic approximation does not require pooling. The computed statistic isSince $9.02<12.59$, do not reject fairness at the 5% level. The approximate $p$-value is $0.172$. This conclusion concerns agreement with the specified independent fair-coin count model; a nonrejection is not proof of fairness.