# Die roll and hypothesis testing

First of all this is not a homework or an assignment; it's an exam question that I couldn't solve.

"There is a $$4$$-sided die that has the same probability of showing up for each face when rolled, namely $$p_1=p_2=p_3=p_4$$.

It is wanted to test the hypothesis

\begin{align} H_0 &= \text{Die is unbiased} \\ H_1 &= \text{Die is biased}\end{align}

with the procedure of stopping to roll if the all the faces were equal after four rolls (like $$\{1,1,1,1\}$$). Use significance level $$\alpha = 5\%~$$.

In similar questions we had observed values/frequencies of the rolls and would use the Chi-square test to check whether the die is biased. However now we have just a terminating condition of having same face value when rolled four times.

Since I couldn't build the intuition I don't have any starting point. Any help/guidance would be extremely appreciated.

Thanks in advance.

• What exactly is your question? – Saketh Malyala Apr 30 at 6:54