GCSE - WordPress.com18 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

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

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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]


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

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Second discFirst disc

3. [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)


4. [5 marks]


May 2016, 3HR Q14: 5 Marks

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Blue

Red

White

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Blue

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]



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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)


Pass

Fail.. . . . . . . . . .

0.7

6. [7 marks]


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.


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)


7. [6 marks]


June 2015, 4H Q15: 6 Marks

15

*P43075A01524* Turn over

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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.

.. . . . . . . . . . . . . . . . . . . . . . . . . . .

(3)


Bag A Bag B

White57

8. [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]


June 2016, 4H Q16: 7 Marks

17


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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)


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)


Do NOT write in this space.

10. [5 marks]


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

.. . . . . . . . . . .

Second attempt

Clear

Not clear

0.4

.. . . . . . . . . . .

Third attempt

Clear

Not clear.. . . . . . . . . . .

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11. [6 marks]


January 2014, 4HR Q17: 6 Marks

19


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)


15


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


(3)

(b) Calculate the probability that Boris wins the match.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(3)


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]



15


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.


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)


13. [6 marks]


May 2012, 4H Q18: 6 Marks

Documents

GCSE - WordPress.com18 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