4. You have a deck of 18 cards, with: 10 cards that are white on both sides; 5 cards that are white on one side, black on the other; 3 cards that are black on both sides. The cards are shuffled and randomly flipped. You draw one card at random from the deck and look only at one side of it. Hint: Be careful! Each side of the card counts as a separate outcome. Think about it in terms of the 36 sides that are possible (not the 18 possible cards). (a) Draw a tree diagram with the probabilities of all possible card types. Your tree should have two levels, one for the color of the top of the card, and one for the color of the bottom of the card. It should also include all of the joint probabilities (top color AND bottom color) at the ends. (b) What is the probability that the top of your card is white? (c) If the top of your card is black, what is the probability that the bottom is white? (d) What is the probability that the bottom of your card is black? Show how you got this.