The game SET is played with a deck of cards. Each card has one, two, or three symbols; each symbol is red, green, or purple; each symbol is shaded, open, or filled; and each symbol is a diamond, oval, or squiggle. There is exactly one card with each possible combination of attributes.
(a) How many SET cards are there?
(b) Draw a card from the SET deck. What is the probability that . . .
(i) . . . the card has three symbols?
(ii) . . . the card is shaded?
(iii) . . . the card is shaded and has three symbols?
(iv) . . . the card is shaded or has three symbols?
(c) Are three-ness and shaded-ness independent events or not?
(d) Draw two cards. What is the probability that both cards have filled symbols?
(e) Draw two cards. What is the probability that at least one card is green?
(f) Draw two cards. What is the probability that at least one card has two diamonds?
(g) Draw two cards. Use conditional probability to determine whether or not the first card being green is independent of the second card having two diamonds. (Think carefully. Does it matter whether the second card is green? Whether the first card has two diamonds?)
(h) Draw two cards. Use conditional probability to determine whether or not both cards having filled symbols is independent of at least one card being green.
(i) If you have never before played SET, go find a deck and learn how to play it. SET is way fun!