CAIE IGCSE Mathematics Extended E8.4 Conditional Probability Topic Practice

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Question 1

[Maximum number: 2]
Figure for Question 1 — CAIE IGCSE Mathematics Extended

50 students are asked if they like English ( E ) and if they like mathematics ( M ). 3 say they do not like English and do not like mathematics.
33 say they like English.
42 say they like mathematics.

Two students who like English are chosen at random.

Find the probability that they both also like mathematics.

Question 2

[Maximum number: 2]

This year, 40 students have each travelled by one or more of plane (P), train (T) or boat (B).
7 have travelled only by plane.
11 have travelled only by train.
9 have travelled only by boat.

n(P∩T)=8n(B∩T)=3n(B∩P)=6\begin{aligned} & \mathrm{n}(P \cap T)=8 \\ & \mathrm{n}(B \cap T)=3 \\ & \mathrm{n}(B \cap P)=6 \end{aligned}
Figure for Question 2 — CAIE IGCSE Mathematics Extended

Two students are chosen at random from those who have travelled by train.

Calculate the probability that they both have also travelled by plane.

Question 3

[Maximum number: 2]
Dice A

Dice A

Dice B

Dice B

The diagram shows two fair dice.
Dice A is numbered 1,2,2,2,3,6.
Dice B is numbered 2,3,3,4,4,4.

Dice A and Dice B are each rolled once.

Find the probability that when the two numbers they land on have a total of 6 , both numbers are 3.

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