gcse - wordpress.com18 bill and jo play some games of table tennis. the probability that bill wins...
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PROBABILITY TREES[ESTIMATED TIME: 70 minutes] GCSE TOPIC PRACTICE
(+ IGCSE) EXAM QUESTION PRACTICE
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1. [8 marks]
Note that these questions are sorted in date order (most recent questions first).
November 2008, 4H Q11: 8 Marks
Questions compiled by @Maths4Everyone
16
*P44620A01624*
13 Jim has a biased coin. The probability that Jim will throw Heads on any throw is p. Jim throws the coin twice.
(a) Complete the probability tree diagram. Give your probabilities in terms of p.
Heads
Tails.. . . . . . . . . . . . . . . . . . .
Heads
Tails.. . . . . . . . . . . . . . . . . . .
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Heads
Tails
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p
First throw Second throw
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(2)
(b) Find an expression, in terms of p, for the probability that Jim will throw two Heads.
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(1)
Given that p = 0.8,
(c) work out the probability that Jim will throw exactly one Head.
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(3)
(Total for Question 13 is 6 marks)
2. [6 marks]
Note that these questions are sorted in date order (most recent questions first).
January 2015, 4HR Q13: 6 Marks
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14 *N23069A01420*
13. A bag contains 1 red disc, 2 blue discs and 3 green discs.
Xanthe chooses a disc at random from the bag. She notes its colour and replaces it.Then Xanthe chooses another disc at random from the bag and notes its colour.
(a) Complete the probability tree diagram showing all the probabilities.
(3)
R
16
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Second discFirst disc
3. [8 marks]
Note that these questions are sorted in date order (most recent questions first).
November 2005, 4H Q13: 8 Marks
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(b) Calculate the probability that both discs are the same colour.
..........................(3)
(c) Calculate the probability that neither disc is red.
..........................(2)
14. The volume of oil in a tank is 1000 litres, correct to the nearest 10 litres. The oil is poured into tins of volume 2.5 litres, correct to one decimal place.
Calculate the upper bound of the number of tins which will be required.
........................................Q14
(Total 3 marks)
Q13
(Total 8 marks)
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14 Linford and Alan race against each other in a competition.
If one of them wins a race, he wins the competition. If the race is a draw, they run another race.
They run a maximum of three races.
Each time they race, the probability that Linford wins is 0.35 Each time they race, the probability that there is a draw is 0.05
(a) Complete the probability tree diagram.
race 1 race 2 race 3
Linfordwins
draw
Alanwins
Linfordwins
draw
Alanwins
0.35
0.05
Linfordwins
draw
Alanwins
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(2)
(b) Calculate the probability that Linford wins the competition.
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(3)
(Total for Question 14 is 5 marks)
4. [5 marks]
Note that these questions are sorted in date order (most recent questions first).
May 2016, 3HR Q14: 5 Marks
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Blue
Red
White
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Red
White
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Red
White
Blue
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Red
White
Blue
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Colour offirst bead
Colour ofsecond bead
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5. [6 marks]
Note that these questions are sorted in date order (most recent questions first).
November 2010, 4H Q14: 6 Marks
12
*P42941A01220*
14 Peter wants to pass his driving test. The probability that he passes at his first attempt is 0.7 When Peter passes his driving test, he does not take it again. If he fails, the probability that he passes at the next attempt is 0.8
(a) Complete the probability tree diagram for Peter’s first two attempts.
First attempt Second attempt
(2)
(b) Calculate the probability that Peter needs exactly two attempts to pass his driving test.
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(2)
(c) Calculate the probability that Peter passes his driving test at his third or fourth attempt.
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(3)
(Total for Question 14 is 7 marks)
Pass
Fail.. . . . . . . . . .
0.7
6. [7 marks]
Note that these questions are sorted in date order (most recent questions first).
January 2014, 4H Q14: 7 Marks
14
*P44389A01424*
15 There are 6 milk chocolates and 4 plain chocolates in a box. Rob takes at random a chocolate from the box and eats it. Then Alison takes at random a chocolate from the box and eats it.
(a) Complete the probability tree diagram.
milk chocolate
plain chocolate.. . . . . . . . . . . . . . . . . . .
milk chocolate
plain chocolate.. . . . . . . . . . . . . . . . . . .
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milk chocolate
plain chocolate.. . . . . . . . . . . . . . . . . . .
Rob Alison
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(3)
(b) Work out the probability that there are now exactly 3 plain chocolates in the box.
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(3)
(Total for Question 15 is 6 marks)
7. [6 marks]
Note that these questions are sorted in date order (most recent questions first).
June 2015, 4H Q15: 6 Marks
15
*P43075A01524* Turn over
15 Maria has two bags. ,Q�EDJ�$��WKHUH�DUH���ZKLWH�FRXQWHUV�DQG���UHG�FRXQWHUV� ,Q�EDJ�%��WKHUH�DUH���ZKLWH�FRXQWHUV�DQG���UHG�FRXQWHUV�
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(2)
(b) Work out the probability that both counters will be white.
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(2)
(c) Work out the probability that exactly one of the counters will be white.
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(3)
(Total for Question 15 is 7 marks)
Bag A Bag B
White57
8. [7 marks]
Note that these questions are sorted in date order (most recent questions first).
May 2014, 4HR Q15: 7 Marks
16
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16 In a bag there is a total of 20 coins.
10 coins are 20 cent coins 6 coins are 10 cent coins4 coins are 5 cent coins
Emma takes at random two of the coins from the bag.
(a) Complete the probability tree diagram.(2)
First coin Second coin
20 cent coin
5 cent coin
10 cent coin
1020
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20 cent coin
5 cent coin
10 cent coin
20 cent coin
5 cent coin
10 cent coin
20 cent coin
5 cent coin
10 cent coin
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9. [7 marks]
Note that these questions are sorted in date order (most recent questions first).
June 2016, 4H Q16: 7 Marks
17
*P45863A01724* Turn over
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(b) Work out the probability that Emma takes two 5 cent coins.
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(2)
(c) Work out the probability that the total value of the two coins is 20 cents or less.
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(3)
(Total for Question 16 is 7 marks)
14
*P42070A01420*
17 Parveen travels to school either by bicycle or by bus. The probability that, on any day, she will travel by bicycle is 0.7 When she travels by bicycle, the probability that she will be late for school is 0.2 When she travels by bus, the probability that she will be late for school is 0.1
(a) Calculate the probability that, on a randomly chosen day, Parveen will travel by bus and be late for school.
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(2)
(b) Calculate the probability that, on a randomly chosen day, Parveen will not be late for school.
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(3)
(Total for Question 17 is 5 marks)
Do NOT write in this space.
10. [5 marks]
Note that these questions are sorted in date order (most recent questions first).
May 2013, 3H Q17: 5 Marks
18
*P43131A01824*
17 Hugo competes in the high jump at a school athletics competition. He has up to 3 attempts to clear the bar at each height. When he clears the bar, he does not have another attempt at that height.
When the bar is set at a height of 1.60 metres, the probability that Hugo will clear the bar on any attempt is 0.4
The probability tree diagram shows the possible outcomes of Hugo’s attempts at 1.60 metres.
(a) Complete the probability tree diagram to show the four missing probabilities.(1)
(b) Work out the probability that Hugo does not clear the bar on his first two attempts and then does clear the bar on his third attempt at 1.60 metres.
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(2)
First attempt
Clear
Not clear
0.4
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Second attempt
Clear
Not clear
0.4
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Third attempt
Clear
Not clear.. . . . . . . . . . .
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11. [6 marks]
Note that these questions are sorted in date order (most recent questions first).
January 2014, 4HR Q17: 6 Marks
19
*P43131A01924* Turn over
Hugo clears the bar at 1.60 metres and the height is raised to 1.65 metres. He has up to three attempts to clear the bar at 1.65 metres.
When the bar is set at a height of 1.65 metres, the probability that Hugo will clear the bar on any attempt is 0.3
(c) Find the probability that Hugo clears the bar at 1.65 metres.
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(3)
(Total for Question 17 is 6 marks)
15
*P42933A01520* Turn over
18 Boris and Nigel play games of chess against each other in a match. In each game, Boris wins or Nigel wins or the game is a draw.
When a player wins a game, he wins the match. When a game is a draw, the players play another game against each other. Boris and Nigel play a maximum of 3 games.
The probability that Boris wins a game is 13
The probability that a game is a draw is 12
(a) Complete the probability tree diagram.
(3)
(b) Calculate the probability that Boris wins the match.
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(3)
(Total for Question 18 is 6 marks)
Draw
13
12
Boris wins
Nigel wins.. . . . . . . . . . . . .
First game
Draw
Boris wins
Nigel wins
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Second game
Draw
Boris wins
Nigel wins
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Third game
12. [6 marks]
Note that these questions are sorted in date order (most recent questions first).
May 2013, 3HR Q18: 6 Marks
15
*P40661A01520* Turn over
18 Bill and Jo play some games of table tennis. The probability that Bill wins the first game is 0.7 When Bill wins a game, the probability that he wins the next game is 0.8 When Jo wins a game, the probability that she wins the next game is 0.5
The first person to win two games wins the match.
(a) Complete the probability tree diagram.
Bill wins
Bill wins
Jo wins
Jo wins
Bill wins
Jo wins
Bill wins
Jo wins
Bill wins
Jo wins
0.7
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First game Second game Third game
(3)
(b) Calculate the probability that Bill wins the match.
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(3)
(Total for Question 18 is 6 marks)
13. [6 marks]
Note that these questions are sorted in date order (most recent questions first).
May 2012, 4H Q18: 6 Marks