Biased coin check How many trials are needed to decide with 50% confidence that a coin is biased?
I suspect there is some missing information. Any ideas / pointers?
 A: This is  a "hypothesis testing" problem of roughly standard shape. However, the figure of $50\%$ makes no practical sense at all in this context.
We have the null hypothesis $H_0$ that says the coin is unbiased, and the alternate hypothesis $H_1$ that says the coin is biased. The test is two-sided, since the alternate hypothesis makes no reference to the direction of the bias. 
Suppose that we toss the coin $n$ times. We will reject the null hypothesis in favour of the alternate hypothesis if, assuming the coin is fair, the proportion of heads we got would happen less than $50\%$ of the time. 
Let $n=2$ and suppose that we reject the null hypothesis if we get $2$ heads or $2$ tails. With a fair coin, this would happen exactly $50\%$ of the time. So perhaps $n=2$ is the intended answer. However, a more sensible answer (to a quite unreasonable question) is to take $n=3$, and to reject the null hypothesis if we get $3$ heads or $3$ tails. Then, when the null hypothesis is true, we will reject it with probability $\frac{1}{8}+\frac{1}{8}$, which is under $50\%$.
Remark: Traditionally, one rejects the null hypothesis $H_0$ in favour of $H_1$ if, on the hypothesis that $H_0$ is true, the experimental result has probability $\lt 5\%$ of happening. Or else one may use the more stringent $1\%$ criterion. The figure of $50\%$ makes no practical sense: obviously one would not reject the hypothsis that a coin is fair if we got $3$ heads or $3$ tails.  
