Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Indeterminism wikipedia , lookup
History of randomness wikipedia , lookup
Random variable wikipedia , lookup
Probability box wikipedia , lookup
Infinite monkey theorem wikipedia , lookup
Inductive probability wikipedia , lookup
Birthday problem wikipedia , lookup
Conditioning (probability) wikipedia , lookup
Ars Conjectandi wikipedia , lookup
PROBABILITY TREE DIAGRAMS Name: _______________________ Total Marks: ___________ Q. 1 2 3 4 5 6 7 8 9 10 11 www.justmaths.co.uk Max Actual RAG 4 6 4 4 5 4 3 ©JustMaths 2013 Q1. At the end of a training course candidates must take a test in order to pass the course. The probability of passing the test at the first attempt is 0.8 Those who fail will resit once. The probability of passing the resit is 0.5 and no further attempts are allowed. a) Complete the tree diagram, which shows all possible outcomes. (1 Mark) b) What is the probability that a candidate fails both attempts and so fails the course? (2 Marks) c) What is the probability that a candidate passes the course? (1 Mark) www.justmaths.co.uk ©JustMaths 2013 Q2. A bag contains 5 green and 3 red balls. A ball is taken from the bag at random and replaced. Another ball is then taken from the bag at random. Complete the tree diagram. (1 Mark) b) What is the probability that both balls are red? (2 Marks) c) Some more green balls are added to the 5 green and 3 balls in the bag. A ball is taken from the bag at random and replaced. Another ball is then taken from the bag at random. The probability that both balls are red is now How many green balls were added to the bag? (3 Marks) www.justmaths.co.uk ©JustMaths 2013 Q3. A bag contains 6 blue ad 4 white balls. A ball is taken at random and replaced. Another ball is then taken from the bag at random. (1 Mark) a) Complete the tree diagram. b) What is the probability that both balls are the same colour? (3 Marks) www.justmaths.co.uk ©JustMaths 2013 Q4. These ten letters are placed in a hat: S T A T I S T I C S A letter is drawn from the hat at random, noted and replaced. Another letter is drawn from the hat at random and noted. a) Complete the tree diagram to show whether or not the letters drawn are vowels (A or I) or consonants (C, S or T). (1 Mark) b) Work out the probability that at least one of the letters drawn is a vowel. (3 Marks) www.justmaths.co.uk ©JustMaths 2013 Q5. Two ordinary six-sided dice are used in a game. One dice is fair and the other is biased. The probability of throwing a six with the biased dice is p. The two dice are thrown. The probability of getting exactly one six is Using the tree diagram or otherwise, work out p. (5 Marks) www.justmaths.co.uk ©JustMaths 2013 Q6. In a game of chess, a player can win, draw or lose. The probability that Vishi wins any game of chess is 0.5 The probability that Vishi draws any game of chess is 0.3 Vishi plays 2 games of chess. a) Complete the probability tree diagram. (2 Marks) b) Work out the probability that Vishi will win both games. (2 Marks) www.justmaths.co.uk ©JustMaths 2013 Q7. Two fair coins are thrown. Ahmed says “the probability of obtaining two tails is less than 0.5”. Is Ahmed correct? You must show all the necessary working to justify your answer. (3 Marks) www.justmaths.co.uk ©JustMaths 2013