Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk E8 Probability Question Paper Level Subject Exam Board Level Topic Booklet IGCSE Maths (0580) Cambridge International Examinations (CIE) Extended E8. Probability Question Paper 75 minutes Time Allowed: Score: / 62 Percentage: /100 Grade Boundaries: A* A B C D E U >85% 75% 60% 45% 35% 25% <25% Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk 8 1. The probability of a cricket team winning or losing in their first two matches is shown in the tree diagram. First match 1 3 2 3 Second match 3 4 win 1 4 lose 3 4 win win lose lose Find the probability that the cricket team wins at least one match. ................................................... [3] Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk 2. Kiah plays a game. The game involves throwing a coin onto a circular board. Points are scored for where the coin lands on the board. 5 10 20 If the coin lands on part of a line or misses the board then 0 points are scored. The table shows the probabilities of Kiah scoring points on the board with one throw. Points scored 20 10 5 0 Probability x 0.2 0.3 0.45 (a) Find the value of x. x = ................................................. [2] (b) Kiah throws a coin fifty times. Work out the expected number of times she scores 5 points. .................................................. [1] Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk (c) Kiah throws a coin two times. Calculate the probability that (i) she scores either 5 or 0 with her first throw, .................................................. [2] (ii) she scores 0 with her first throw and 5 with her second throw, .................................................. [2] (iii) she scores a total of 15 points with her two throws. .................................................. [3] (d) Kiah throws a coin three times. Calculate the probability that she scores a total of 10 points with her three throws. .................................................. [5] Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk 3. Hattie has a box of coloured pens. She takes a pen at random from the box. The probability that she takes a red pen is 0.4 . (a) Work out the probability that she does not take a red pen. .................................................. [1] (b) The box contains only blue, red and green pens. There are 15 blue pens and 15 green pens. Complete the table. Colour of pen Number of pens Blue Red 15 Probability Green 15 0.4 [2] 4 Coins are put into a machine to pay for parking cars. The probability that the machine rejects a coin is 0.05 . (a) Adhira puts 2 coins into the machine. (i) Calculate the probability that the machine rejects both coins. ................................................... [2] (ii) Calculate the probability that the machine accepts at leastone coin. ................................................... [1] Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk (b) Raj puts 4 coins into the machine. Calculate the probability that the machine rejects exactlyone coin. ................................................... [3] (c) The table shows the amount of money, $a, received for parking each day for 200 days. 200 1 a G 250 250 1 a G 300 300 1 a G 350 350 1 a G 400 400 1 a G 450 450 1 a G 500 13 19 27 56 62 23 Calculate an estimate of the mean amount of money received each day. $ ................................................... [4] Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk (d) The histogram shows the length of time that 200 cars were parked. 1.2 1.1 1 0.9 0.8 0.7 Frequency density 0.6 0.5 0.4 0.3 0.2 0.1 0 50 100 150 200 250 300 350 400 Time in minutes (i) Calculate the number of cars that were parked for 100 minutes or less. ................................................... [1] (ii) Calculate the percentage of cars that were parked for more than 250 minutes. ...............................................% [2] Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk 5. Dan either walks or cycles to school. The probability that he cycles to school is 13 . (a) Write down the probability that Dan walks to school. ................................................... [1] (b) When Dan cycles to school the probability that he is late is 18 . When Dan walks to school the probability that he is late is 38 . Complete the tree diagram. 1 8 1 3 Cycles .......... 3 8 .......... Late Not late Late Walks .......... Not late [2] (c) Calculate the probability that (i) Dan cycles to school and is late, ................................................... [2] (ii) Dan is not late. ................................................... [3] Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk 6 Paul and Sammy take part in a race. The probability that Paul wins the race is 9 35 . The probability that Sammy wins the race is 26%. Who is more likely to win the race? Give a reason for your answer. Answer ........................... because .............................................................................................................. [2] 7 A biased 4-sided dice is rolled. The possible scores are 1, 2, 3 or 4. The probability of rolling a 1, 3 or 4 is shown in the table. Score Probability Complete the table. 1 0.15 2 3 4 0.3 0.35 [2] Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk 8 Gareth has 8 sweets in a bag. 4 sweets are orange flavoured, 3 are lemon flavoured and 1 is strawberry flavoured. (a) He chooses two of the sweets at random. Find the probability that the two sweets have different flavours. Answer(a) ................................................ [4] (b) Gareth now chooses a third sweet. Find the probability that none of the three sweets is lemon flavoured. Answer(b) ................................................ [2] Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk 9 A A A A B B C (a) One of these 7 cards is chosen at random. Write down the probability that the card (i) shows the letter A, (ii) shows the letter A or B, (iii) does not show the letter B. Answer(a)(i) ................................................. [1] Answer(a)(ii) ................................................. [1] Answer(a)(iii) ................................................. [1] (b) Two of the cards are chosen at random, without replacement. Find the probability that (i) both show the letter A, Answer(b)(i) ................................................. [2] Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk (ii) the two letters are different. Answer(b)(ii) ................................................. [3] (c) Three of the cards are chosen at random, without replacement. Find the probability that the cards do not show the letter C. Answer(c) ................................................. [2]
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