GCSE Exams Preparation



Probability Tree (H) - QuestionsQ1.?The diagram shows a fair 4-sided spinner.Hasmeet is going to spin the spinner twice.(a)??Complete the probability tree diagram.(2)(b)??Work out the probability that the spinner will land on A on the first spin and will land on B on the second spin. ........................................................... (2)?(Total for question = 4 marks)?Q2.?*Shabeen has a biased coin. The probability that the coin will land on heads is 0.6Shabeen is going to throw the coin 3 times.She says the probability that the coin will land on tails 3 times is less than 0.1Is Shabeen correct? You must show all your working.(Total for Question is 3 marks)Q3.?The probability tree diagram shows the probabilities that Bismah will be late for work on two days next week.Calculate the probability that Bismah will be late on exactly one of the two days. ........................................................... ?(Total for question = 3 marks)?Q4.?There are only r red counters and g green counters in a bag.A counter is taken at random from the bag.The probability that the counter is green is The counter is put back in the bag.2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag.The probability that the counter is green is Find the number of red counters and the number of green counters that were in the bag originally.red counters ........................................................... green counters ........................................................... ?(Total for question = 5 marks)?Q5.?Alan has two spinners, spinner A and spinner B. Each spinner can land on only red or white.The probability that spinner A will land on red is 0.25 The probability that spinner B will land on red is 0.6The probability tree diagram shows this information.Alan spins spinner A once and he spins spinner B once. He does this a number of times.The number of times both spinners land on red is 24Work out an estimate for the number of times both spinners land on white. ........................................................... ?(Total for question = 3 marks)?Q6.?Mary travels to work by train every day. The probability that her train will be late on any day is 0.15(a)??Complete the probability tree diagram for Thursday and Friday.(2)(b)??Work out the probability that her train will be late on at least one of these two days. ........................................................... (3)?(Total for question = 5 marks)?Q7.?A darts team is going to play a match on Saturday and on Sunday. The probability that the team will win on Saturday is 0.45If they win on Saturday, the probability that they will win on Sunday is 0.67 If they do not win on Saturday, the probability that they will win on Sunday is 0.35(a)??Complete the probability tree diagram.(2)(b)??Find the probability that the team will win exactly one of the two matches. ........................................................... (3)?(Total for question = 5 marks)?Q8.?Seb has a biased dice.When the dice is thrown once, the probability that it will land on 6 is Seb is going to throw the dice twice.(a) ?Complete the probability tree diagram.(2)(b) ?Work out the probability that the dice will land on 6 on the first throw and will not land on 6 on the second throw............................................................(2)?(Total for question = 4 marks)?Q9.?Sameena has a round pencil case and a square pencil case.There are 4 blue pens and 3 red pens in the round pencil case. There are 3 blue pens and 5 red pens in the square pencil case.Sameena takes at random one pen out of each pencil case.(a)??Complete the probability tree diagram.(2)(b)??Work out the probability that the pens Sameena takes are both red. ........................................................... (2)?(Total for question = 4 marks)?Q10.?Louise makes a spinner.The spinner can land on green or on red. The probability that the spinner will land on green is 0.7Louise spins the spinner twice.(a) ?Complete the probability tree diagram.(2)(b) ?Work out the probability that the spinner lands on two different colours............................................................(3)? (Total for question = 5 marks)Q11.The probability that Rebecca will win any game of snooker is p.She plays two games of snooker.(a) Complete, in terms of p, the probability tree diagram.?(2)(b) Write down an expression, in terms of p, for the probability that Rebecca will win both games.??????..............................................................................................................................................(1)(c) Write down an expression, in terms of p, for the probability that Rebecca will win exactly one of the games.??????????..............................................................................................................................................(2)(Total for Question is 5 marks)Q12.?Event A and event B are independent events.The probability that event A will happen is 0.3The probability that event B will happen is 0.6(a) ?Complete the probability tree diagram.(2)(b) ?Work out the probability that either event A will happen or event B will happen but not both............................................................(2)(Total for Question is 4 marks)Q13.?There are 4 banana smoothies and 3 apple smoothies in a box.Jenny takes at random 1 smoothie from the box. She writes down its flavour, and puts it back in the box. Jenny then takes at random a second smoothie from the box.(a) ? Complete the probability tree diagram.(2)(b) ? Work out the probability that both smoothies are apple flavour............................................................(2)(Total for Question is 4 marks)Q14.The probability that it will rain on Monday is 0.6When it rains on Monday, the probability that it will rain on Tuesday is 0.8 When it does not rain on Monday, the probability that it will rain on Tuesday is 0.5?(a) Complete the probability tree diagram.(2)(b) Work out the probability that it will rain on both Monday and Tuesday.????????..............................................................................................................................................(2)(c) Work out the probability that it will rain on at least one of the two days.????????..............................................................................................................................................(3)(Total for Question is 7 marks)Q15.In a newsagent's shop, the probability that any customer buys a newspaper is 0.6In the same shop, the probability that any customer buys a magazine is 0.3(a) Complete the probability tree diagram.(2)(b) Work out the probability that a customer will buy either a newspaper or a magazine but not both.???. . . . . . . . . . . . . . .(3)(Total for Question is 5 marks)Q16.Martin and Luke are students in the same maths class.The probability that Martin will bring a calculator to a lesson is 0.8The probability that Luke will bring a calculator to a lesson is 0.6(a) Complete the probability tree diagram.(2)(b) Work out the probability that both Martin and Luke will not bring a calculator to a lesson.??????????????..............................................................................................................................................(2)(Total for Question is 4 marks)Q17.There are 10 socks in a drawer.7 of the socks are brown.3 of the socks are grey. Bevan takes at random two socks from the drawer at the same time.(a) Complete the probability tree diagram.(2)(b) Work out the probability that Bevan takes two socks of the same colour.????????. . . . . . . . . . . . . . . . . . . . . . (3)(Total for Question is 5 marks)Q18.?The probability that it will rain on a day in June is 0.2When it rains the probability that my tennis match is cancelled is 0.7When it does not rain, the probability that my tennis match is not cancelled is 0.95(a)??Complete the probability tree diagram for this information.(3)(b)??Work out the probability that, on a day in June, it does not rain and my tennis match is cancelled. ........................................................... (2)?(Total for question = 5 marks)?Q19.?Kelvin and Mamady are in the same class. The probability that Kelvin arrives on time is 0.7 The probability that Mamady arrives on time is 0.9Complete the probability tree diagram.? (Total for question = 2 marks)Q20.?A and B are two sets of traffic lights on a road.The probability that a car is stopped by lights A is 0.4If a car is stopped by lights A, then the probability that the car is not stopped by lights B is 0.7If a car is not stopped by lights A, then the probability that the car is not stopped by lights B is 0.2(a) ?Complete the probability tree diagram for this information.(2)Mark drove along this road. He was stopped by just one of the sets of traffic lights.(b) ?Is it more likely that he was stopped by lights A or by lights B? You must show your working.(3)? (Total for question = 5 marks)Q21.?Graham has a fair red 6-sided dice and a fair blue 8-sided dice. The red dice can land on 1, 2, 3, 4, 5 or 6 The blue dice can land on 1, 2, 3, 4, 5, 6, 7 or 8Graham is going to roll both dice.(a)??Complete the probability tree diagram.(2)(b)??Work out the probability that neither dice will land on a 6 ........................................................... (2)?(Total for question = 4 marks)?Q22.?Machine A and machine B make bottles.The probability that a bottle made by machine A is faulty is 0.02 The probability that a bottle made by machine B is faulty is 0.05(a)??Complete the probability tree diagram.(2)Shazia takes at random one bottle made by machine A and one bottle made by machine B.(b)??Work out the probability that at least one of these bottles is faulty. ........................................................... (3)?(Total for question = 5 marks)?Q23.?There are 8 counters in a box. The letter A is on 6 of the counters. The letter B is on the other 2 counters.Sally takes at random a counter from the box. She keeps the counter. Then Tina takes at random a counter from the box.(a) ?Complete the probability tree diagram.Sally ???????????????????Tina(3)(b) ?Work out the probability that both Sally and Tina take a counter with the letter A on it............................................................(2)(c) ?Work out the probability that at least one counter with the letter A on it is taken............................................................(3)? (Total for question = 8 marks)Q24.Wendy goes to a fun fair.She has one go at Hoopla.She has one go on the Coconut shy.The probability that she wins at Hoopla is 0.4The probability that she wins on the Coconut shy is 0.3(a) Complete the probability tree diagram.(2)(b) Work out the probability that Wendy wins at Hoopla and also wins on the Coconut shy.??????..............................................................................................................................................(2)(Total for Question is 4 marks)Q25.?Yvonne has 10 tulip bulbs in a bag.7 of the tulip bulbs will grow into red tulips. 3 of the tulip bulbs will grow into yellow tulips.Yvonne takes at random two tulip bulbs from the bag. She plants the bulbs.(a) Complete the probability tree diagram.(2)(b) Work out the probability that at least one of the bulbs will grow into a yellow tulip............................................................(3)(Total for Question is 5 marks)Q26.Lily and Anna take a test.The probability that Lily will pass the test is 0.6The probability that Anna will pass the test is 0.8(a) Work out the probability that both of these girls fail the test.???????????..............................................................................................................................................(3)(b) Work out the probability that both of these girls pass the test or that both of these girls fail the test.??????????..............................................................................................................................................(3)(Total for Question is 6 marks)Q27.There are ten pens in a box. 4 of the pens are red. 6 of the pens are black. Josh takes at random a pen from the box. He puts the pen into his bag. He then takes at random another pen from the box.Work out the probability that Josh takes one pen of each colour.???????????????..............................................................................................................................................(Total for Question is 4 marks)Q28.Isobel plays a game against Eric.Isobel is twice as likely as Eric to win the game.The probability that the game is drawn is 0.1(a) Work out the probability that Eric wins the game.????. . . . . . . . . . . . . . . . . . . . . .(2)Isobel and Eric play the game three times.(b) Work out the probability that all three games are drawn.????. . . . . . . . . . . . . . . . . . . . . .(2)??????(c) Work out the probability that Eric wins at least one of the three games.???????. . . . . . . . . . . . . . . . . . . . . .(3)(Total for Question is 7 marks)Q29.?When a biased 6-sided dice is thrown once, the probability that it will land on 4 is 0.65 The biased dice is thrown twice.Amir draws this probability tree diagram. The diagram is not correct.Write down two things that are wrong with the probability tree diagram.1 .......................................................................................................................................... ............................................................................................................................................. 2 .......................................................................................................................................... ............................................................................................................................................. ?(Total for question = 2 marks)?Q30.?Finlay plays two tennis matches.The probability that he will win a match and the probability that he will lose a match are shown in the probability tree diagram.(a) ?Work out the probability that Finlay wins both matches............................................................(2)(b) ?Work out the probability that Finlay loses at least one match............................................................(2)? (Total for question is 4 marks) ................
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