Tree Diagrams & Combined Probability (Edexcel GCSE Maths: Foundation)

Exam Questions

53 mins14 questions
1a
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2 marks

Tom gets a bus at the same time each morning to go to work.

He gets a bus at the same time each evening to come home.

The probability tree diagram shows the probabilities of each bus arriving late.

Complete the probability tree diagram.

Tree diagram showing the probability of the bus to work being late or not late and the bus home being late or not late

1b
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2 marks

For a day that Tom goes to work, calculate the probability that the bus to work and the bus home will both arrive late.

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2a
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2 marks

William has two boxes of apples.

In the first box there are 4 red apples and 7 green apples.
In the second box there are 6 red apples and 9 green apples.

William takes at random an apple from the first box.
He then takes at random an apple from the second box.

Complete the probability tree diagram.

Tree diagram with two branches (Red - 4/11 and Green - unlabelled probability) for the first box and a second set of branches (Red - 6/15 and Green - unlabelled probability) for the second box

2b
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2 marks

Find the probability that William selects a green apple from each box.

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3
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2 marks

On any day the probability that it rains is 1 third.

When it rains the probability that Amira goes fishing is 3 over 5.
When it does not rain the probability that Amira goes fishing is 3 over 4.

Complete the tree diagram.

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4
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4 marks

On any Saturday, the probability that Arun plays football is 3 over 4.
On any Saturday, the probability that Bob plays football is 2 over 5.

i)

Complete the tree diagram.

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[2]

ii)

Calculate the probability that, one Saturday, Arun and Bob both play football.
 

[2]

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1
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2 marks

When a biased 6-sided dice is thrown once, the probability that it will land on 6 is 0.3.

The biased dice is thrown twice.

Sophie draws this probability tree diagram.

The diagram is not correct.

Write down two things that are wrong with the probability tree diagram.

tree-diagrams-medium-q1

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2a
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2 marks

On Amelia's route to work, she drives through a set of traffic lights.
She also has to cross a bridge, which is sometimes closed to cars.

The probability that the traffic lights will be red when she reaches them is 0.4.

The probability that the bridge is closed when she reaches it is 0.1.

Complete the probability tree diagram below.

Probability tree diagram with a first set of branches for the traffic lights being Red or Not Red and a second set of branches for the bridge being Closed or Not Closed

2b
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2 marks

Find the probability of the traffic lights being red, and the bridge not being closed.

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3
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3 marks

A fair dice with 6 faces, labelled 1 to 6, is rolled twice.

Find the probability of not rolling a 1 on either of the rolls.

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4a
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2 marks

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 0.4
The probability that she wins on the Coconut shy is 0.3

Complete the probability tree diagram.

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4b
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2 marks

Work out the probability that Wendy wins at Hoopla and also wins on the Coconut shy.

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5
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2 marks

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.

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Write down two things that are wrong with the probability tree diagram.

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1a
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2 marks

Priya is at a fairground where she plays different games.

She plays 1 game of hook-a-duck, and then plays 1 game of balloon darts.

The probability of her winning in hook-a-duck is 0.6.

The probability of her winning in balloon darts is 0.45.

Complete the probability tree diagram below.

Probability tree diagram, first pair of branches for the Hook-a-duck game with Win and Not Win and the second set of branches for the Balloon Darts game with Win and Not Win

1b
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3 marks

Find the probability that Priya wins at least 1 game.

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2a
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3 marks

Tommy is selecting socks from his drawer to pack for a weekend away.
His drawer contains only black socks, or coloured socks.

Tommy has 8 pairs of black socks, and 10 pairs of coloured socks in his drawer.

He takes one pair of socks out of the drawer, notes the colour, and does not replace them.
He then takes another pair of socks out of the drawer.

Complete the probability tree diagram.

Probability tree diagram, first pair of branches for the first pair of socks being Black or Coloured and the second set of branches for the second set of socks being Black or Coloured

2b
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3 marks

Find the probability that Tommy selects one black pair of socks, and one coloured pair of socks.

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3
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3 marks

The probability of finding a "shiny" card in a pack of trading cards is 0.4.

If 3 packs are purchased, find the probability of finding at least one "shiny" card.

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4a
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3 marks

The probability that it will rain on a day in June is 0.2

When it rains the probability that my tennis match is cancelled is 0.7

When it does not rain, the probability that my tennis match is not cancelled is 0.95

Complete the probability tree diagram for this information.

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4b
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2 marks

Work out the probability that, on a day in June, it does not rain and my tennis match is cancelled.

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5a
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2 marks

Ding is going to play one game of snooker against each of two of his friends, Marco and Judd.

The probability tree diagram gives information about the probabilities that Ding will win or lose each of these two games.

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Work out the probability that Ding will win both games.

5b
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3 marks

Work out the probability that Ding will win exactly one of the games.

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