Two cards will be dealt off the top of a well-shuffled deck. You have a choice: (i) to win $1 if at least one of the two cards is queen. (ii) to win$1 if the first is a queen. Which option is better? Or are they equivalent? Explain.

The chance of A is 1/3; the chance of B is 1/10. True or false, and explain: a) If A and B are independent, they must also be mutually exclusive. b) If A and B are mutually exclusive, they cannot be independent.

Three cards are dealt from a well-shuffled deck. a) Find the chance that all of the cards are diamonds. b) Find the chance that none of the cards are diamonds. c) Find the chance that the cards are not all diamonds.

A pair of dice are thrown. a) Find the chance that both dice show 3 spots. b) Find the chance that both dice show the same number of spots.

Five cards are dealt off the top of a well-shuffled deck. a) Find the chance that the 5th card is the queen of spades. b) Find the chance that the 5th card is the queen of spades, given that the first 4 cards are hearts.

A die is rolled four times. What is the chance that ----- a) all the rolls show 3 or more spots? b) none of the rolls show 3 or more spots? c) not all the rolls show 3 or more spots?