A standard card deck has 52 cards consisting of 26 black and 26 red cards. Three cards are dealt from a shuffled deck, without replacement.
a. True or false: The probability of being dealt three black cards is (1/2) × (1/2) × (1/2) = 1/8. If true, explain why. If false, show how to get the correct probability.
b. Let A = first card red and B = second card red. Are A and B independent? Explain why or why not.
c. Answer parts a and b if each card is replaced in the deck after being dealt.