You have two biased coins. Coin A comes up heads with probabaility ¼. Coin B comes up heads with probability ¾. However, you are not sure which is which so you choose a coin randomly and you flip it. If the flip is heads, you guess that the flipped coin is B; othervise you guess that the flipped coin is A. Let events A and B designate which coin was picked. What is the probability P(C) that your guess is correct?