1. (4 points) You play a card game with a friend where you get to draw one card from a standard deck of 52 cards. Your friend will give you $1 if the card is a number card (2-10), $2 for a face card (K, Q, J) and $3 for an Ace (A). Further, she will pay $1 for a black card ( or *) and $2 for a red card ( or ). For example, if you draw the 80, you get $1 (number card)+ $2 (red card) = $3. (a) (2 points) Suppose that you draw a black card. What is the probability that your friend owes you at least $4? (b) (2 points) Suppose that your friend owes you at least $4 after the card draw. What is the probability that the card you drew was a black card