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 until a head comes up and record the total number of tosses. You want to set up a hypothesis test to check if coin $A$ was chosen.

(a) What is the significance level of a test that rejects $H_0$ if $X\geq8$?
(b) What is the power of the test.