Probability Questions:

18. A game is played in which two coloured dice are rolled once. The six faces of the black die are numbered 5, 7, 8, 10, 11, 14. The six faces of the white die are numbered 3, 6, 9, 12, 13, 15. The player wins if the number on the black die is bigger than the number on the white die.

(a) Calculate the probability of a player winning the game.

(b) Calculate the probability that a player will lose at least once in two consecutive games.

(c) How many games must be played before you have a 90% chance of winning at least one game?

20. In a game, two dice are rolled and the score given is the maximum of the two numbers on the uppermost faces. For example, if the dice show a three and a five, the score is a five.

(c) Find the probability of a six in a single roll of the dice.

(d) Given that one of the dice shows a three, what is the probability of getting a score greater than five?

21. A set of four cards contains two jacks, a queen and a king. Bob selects one card and then, without replacing it, selects another. Find the probability that:

(c) given that one of Bob's cards is a jack, the other one is also.

Answers:

18(a) 4/9 (b) 65/81 (c) 4

20 (c) 11/36 (d) 2/11

21(c) 1/5