GCSE MATHEMATICS Intermediate Tier, topic sheet. PROBABILITY

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1 GCSE MATHEMATICS Intermediate Tier, topic sheet. PROBABILITY. In a game, a player throws two fair dice, one coloured red the other blue. The score for the throw is the larger of the two numbers showing. For example: if the red dice shows and the blue dice shows 2, the score for the throw is ; if the red dice shows 3 and the blue dice shows, the score for the throw is. a) Complete the following table to show all the possible scores. BLUE b) i) What is the probability that a player scores 6? ii) What is the probability that a player scores less than 6? A player wins a prize by getting a score of or less. c) Bob plays the game once. What is the probability that he wins a prize? d) i) 360 people each play the game once. Approximately how many would you expect to win a prize? ii) It costs to play the game once. The prize for winning is.0. If the 360 people each play the game once, approximately how much profit do you expect the game to make? 2. In a game, a player throws two fair dice, one coloured red the other blue. The score for the throw is the difference between the two numbers showing. For example: if the red dice shows and the blue dice shows 2, the score for the throw is 2; if the red dice shows and the blue dice shows 6, the score for the throw is.

2 a) Complete the following table to show all the possible scores. BLUE b) What is the probability that a player scores 2? A player wins a prize by getting a score of less than 2. c) Bob plays the game once. What is the probability that he wins a prize? d) i) 360 people each play the game once. Approximately how many would you expect to win a prize? ii) It costs 0 pence to play the game once. The prize for winning is 20 pence If the 360 people each play the game once, approximately how much profit do you expect the game to make? 3. The probability that it s on any given day is. Two days are selected at random. a) Complete the following tree diagram to show the possible outcomes and their respective probabilities. First day Second day b) Calcu the probability that it s on both days. c) Calcu the probability that it s on only one of the two days.

3 . The probability that Jenny is for school on any one day is. a) Complete the tree diagram to show the possibilities for two consecutive days and the respective probabilities. First day Second day not not not b) Calcu the probability that on two consecutive days she is i) on both occasions, ii) only once.. On a route to school, a bus must pass through two sets of traffic lights. The probability that the bus has to at a set of lights is. a) Complete the tree diagram to show the possible outcomes and the respective probabilities. st set of lights 2 nd set of lights b) Calcu the probability that the bus does not have to at either set of lights. c) Calcu the probability that the bus has to at only one set of lights.

4 SOLUTIONS / ANSWERS.. a) BLUE b) i) of the 36 possible outcomes represent a score of 6 and so answer =. 36 c) ii) or d) i) out of 9 people will win a prize which is the same as 0 out of 90. This is the same (after multiplying by ) as 60 out of 360. Answer = 60. ii) Income = 360 players = 360. Prize money = 60 winners.0 = 20. Thus profit = = {Similar to Q.} a) BLUE b) or. c) or d) i) 60 ii).

5 3. a) First day Second day b) For the probability that it s on both days, follow the branch of the tree. We multiply the two values of and to get an answer of which equals 2. c) For the probability that it only s on one day we identify two possible paths in the tree diagram:, : = 2 { chances in 2}, : = 2 { chances in 2}. Total up to get an answer of 8 2 {a total of 8 chances in 2.}. a) First day Second day 0.7 not 0.7 not {7 chances in 0} 0.7 not b) i) = ii), not : 0.7 = 0.2 not, : 0.7 = 0.2. Total up to get an answer of = 0.2.

6 . a) st set of lights 2 nd set of lights b) P(bus does not have to at either set of lights) = = 0.6. c) For the probability that the bus only has to at one set of lights we identify two possible paths in the tree diagram:, : 0. = 0.2, : 0. = 0.2. Total up to get an answer of 0.8.

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