8. A Dutch Book is some mix of wagers, which can be shown to result in a sure loss (according to the bettor’s beliefs). Consider this situation (The three-card problem): there are three cards, one is red on both sides (RR), the second is red on one side and white on the other (RW), and the third card is white on both sides (WW). A single card is drawn (eyes closed) and tossed into the air.

a. P (RR card selected) = ?

b. P (W-showing) = ?

c. P (not - RR|R - showing) = ?

d. Are the following fair bets or a Dutch Book:
i. You pay $1 – to guess a card You win $3 – if correct ii. R-showing You pay $1 – to guess card You win $2 – if correct iii. Win $1– if R-showing and not RR You lose $1– if R-showing and RR