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.

24. Shadia has invented a game for one person. She throws two dice repeatedly until the sum of the two numbers shown is either six or eight. If the sum is six, she wins. If the sum is eight, she loses. If the sum is any other number, she continues to throw until the sum is six or eight.

(b) What is the probability that a second throw is needed?

(c) Find an expression for the probability that Shadia wins on her first, second or third throw.

(d) Calculate the probability that Shadia wins the game.

28. There are two white and three black discs in a bag. Two players A and B are playing a game in which they draw a disc alternately from the bag and then replace it. Player A must draw a white disc to win and player B must draw a black disc. Player A goes first. Find the probability that:

(d) player A wins the game

Answers:

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

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

21(c) 1/5

24 (b) 13/18 (c) 5/36 + 13/18 5/36 + 5/36 (d)

28 (d) 10/19