Each round the player has to pick 6 cards out of 2 decks of 52 (104 cards in total, everything is doubled) without replacement. Each hand of cards costs 15 points (there's 5 draws):

• 10 points if a spade isn't drawn
• 20 points if 2 spades are drawn
• 0 points if 1 spade is drawn
• 30 points if 3 spades are drawn
• 50 points if 4 spades are drawn

a) do the theoretical probability distribution

b) find the expected value