Suppose that you have two coins $A$ and $B$ in an urn. Coin $A$ has probability of heads equal to $0.5$, and coin $B$ has probability of heads equal to $0.7$. You pick a coin from the urn blind-folded. You now toss it $10$ times and record the number of heads. To check if coin $A$ was chosen, you want to set up a hypothesis test by rejecting the null (that the coin is A) if the number of heads exceeds some constant.

(a)What would your rejection criterion be for a $0.01$ significance level.
(b) Compute the power of the test. (the alternative hypothesis is that the coin is B)

(You may use a calculator or a Binomial table)