John Claims That He Is Mildly Psychic and Can Guess

Short Answer

John claims that he is mildly psychic and can guess the color of a card withdrawn from an ordinary deck of cards correctly 70% of the time. His friend selects cards at random from the deck (replacing them and shuffling each time). He selects 12 cards and John guesses 9 correctly.
(a) Find the probability that John guesses exactly 9 correctly if his claim of being psychic is true.
(b) Find the probability that he gets exactly 9 correct if he is just guessing.