IGCSEMaths: ExtendedCIETopic QuestionsProbabilityConditional Probability

Syllabus Edition

First teaching 2023

First exams 2025

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Conditional Probability (CIE IGCSE Maths: Extended)

Topic Questions

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1
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cie-igcse-2020-oct-nov-p4-tz2-q6a

The diagram shows six discs.
Each disc has a colour and a number.

Two of the six discs are picked at random without replacement.

Find the probability that 

i)
both discs have the number 3,
  
[2]
ii)
both discs have the same colour.
 
[3]

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2
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cie-igcse-2020-oct-nov-p4-tz3-q4a

Morgan picks two of these letters, at random, without replacement.

Find the probability that he picks two letters that are the same.

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3
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A bag contains 5 blue marbles and 2 green marbles.
Bryn picks one marble at random without replacement.
If this marble is not green, he picks another marble at random without replacement.
He continues until he picks a green marble.

Find the probability that he picks a green marble on his first, second or third attempt.

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4
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Esme has a bag with 5 green counters and 4 red counters.
She takes three counters at random from the bag without replacement.
 
Work out the probability that the three counters are all the same colour.

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5a
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cie-igcse-2018-oct-nov-p4-tz3-q7
 

Bag A contains 3 black balls and 2 white balls.
Bag B contains 1 black ball and 3 white balls.
A ball is taken at random from each bag.

i)
Show that a black ball is more likely to be taken from bag A than from bag B.
 
 

[1]

ii)
Find the probability that the two balls have different colours.
 
 

[3]

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5b
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The balls are returned to their original bags.
Three balls are taken at random from bag A, without replacement.

i)
Find the probability that they are all black.
 
 

[2]

ii)
Find the probability that they are all white.
 
 

[1]

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5c
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The balls are returned to their original bags.
A ball is taken at random from bag A and its colour is recorded.
This ball is then placed in bag B.
A ball is then taken at random from bag B.
 
Find the probability that the ball taken from bag B has a different colour to the ball taken from bag A.

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1
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 box enclose space space space 1 space space space end enclose space space space space box enclose space space space 2 space space space end enclose space space space space box enclose space space space 3 space space space end enclose space space space space box enclose space space space 4 space space space end enclose space space space space box enclose space space space 5 space space space end enclose space 

The diagram shows five cards.
Two of the cards are taken at random, without replacement.

Find the probability that both cards show an even number.

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2
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cie-igcse-2020-oct-nov-p4-tz3-q4a

Morgan picks two of these letters, at random, without replacement.

Find the probability that he picks

i)
the letter Y first,

[1]
ii)
the letter B then the letter Y.
 
[2]

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3
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A bag contains 4 red marbles and 2 yellow marbles.
Behnaz picks two marbles at random without replacement.

Find the probability that

i)

the marbles are both red,
 

[2]

ii)

the marbles are not both red.
 

[1]

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1
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cie-igcse-2020-oct-nov-p4-tz3-q4a

Morgan picks three of these letters, at random, without replacement.

Find the probability that

i)
all three letters are the same,
 
[2]
ii)
exactly two of the three letters are the same,
 
[5]
iii)
all three letters are different.
 
[2]

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2
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Suleika has six cards numbered 1 to 6.

cie-igcse-2020-march-p4-tz2-q6a

Suleika takes two cards at random, without replacement.

i)
Find the probability that the sum of the numbers on the two cards is 5.


[3]

ii)
Find the probability that at least one of the numbers on the cards is a square number.


[3]

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3
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cie-igcse-2019-oct-nov-p4-tz1-q8

The diagram shows 5 cards.

Donald chooses two of the five cards at random, without replacement.
He works out the total number of dots on these two cards.

i)
Find the probability that the total number of dots is 5.

[3]

ii)
Find the probability that the total number of dots is an odd number.

[3]

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4a
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Angelo has a bag containing 3 white counters and x black counters.
He takes two counters at random from the bag, without replacement.

Complete the following statement.
 
The probability that Angelo takes two black counters is fraction numerator x over denominator x plus 3 end fraction cross times fraction numerator............ over denominator............ end fraction

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4b
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The probability that Angelo takes two black counters is 7 over 15.

i)
Show that 4 x squared minus 25 x minus 21 equals 0.
 
[4]
ii)
Solve by factorisation 4 x squared minus 25 x minus 21 equals 0.
 
x = .................... or x = ................. [3]
iii)
Write down the number of black counters in the bag.
 
[1]

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