Compute the probabilities for each simple or compound event.

At North American casinos, roulette wheels have 38 total "pockets", two of which are green zeros (0 and 00) where the house collects all (i.e. the player loses). In Europe the rules are similar, but there are only 37 total "pockets", because there is only one green zero (0).

1. Is the probability of hitting the green zero pocket (0 or 00) lower in Europe or

in North America?

In card games such as bridge, cards are shuffled before each deal. The deal usually has a 'memory' of previous games, because shuffling is imperfect. After a deal, cards stay in an order that still reflects the order present before the deal. Even professional dealers are not perfect. A pack must be shuffled at least seven times by a professional to eliminate all traces of its previous order. Suppose some good friends are playing, and they shuffle the pack only twice before each deal.

2. In repeated playing, are the hands that are dealt unbiased?

3. Are they independent?

A card is drawn from a standard deck of 52 cards, consisting of 4 suits (Clubs, Spades, Hearts, Diamonds) each with 13 cards (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King). The deck has been well-shuffled seven times. What is the probability that the card drawn is:

4. Either a face card (jack, queen, king) or a ten?

5. Both a spade and a face card (jack, queen, king)?

(continued)

When two cards are drawn in succession from a standard pack of cards, what are the

probabilities of drawing:

6. Two cards, neither of which is a heart, with replacement?

7. Two cards, neither of which is a heart, without replacement?

Consider that an archer's target has four concentric circles around a bull's-eye. For a certain archer (whose shots are independent), the probabilities of her scoring are as follows:

Pr(hit the bull's-eye) = 1/10 = 0.1 = 10%

Pr(hit first circle, but not bull's-eye) = 3/10 = 0.3 = 30%

Pr(hit second circle, but no better) = 2/10 = 0.2 = 20%

Pr(hit third circle, but no better) = 2/10 = 0.2 = 20%

Pr(hit fourth circle, but no better) = 1/10 = 0.1 = 10%

8. What is the probability that in two shots, she scores a bull's-eye on the first shot, and the

third circle on the second shot?

9. What is the probability that in two shots, she hits the bull's-eye once, and the third

circle once?

10. What is the probability that on any one shot, she misses the target entirely?