CAIE IGCSE Mathematics Extended Probability Question Bank

Practise CAIE IGCSE probability through single and combined events, experimental results, expected frequencies, trees, tables and without-replacement choices.

[Maximum number: 3]

The 200 students also estimate the total area, $A \mathrm{~m}^{2}$ , of the windows in the classroom. The table shows their results.

Table for Question 8. Probability question 1 — CAIE IGCSE Mathematics Extended

Two students are chosen at random from those students that estimated the area of the windows to be more than $100 \mathrm{~m}^{2}$ .

Find the probability that one of the two students estimates the area to be greater than $150 \mathrm{~m}^{2}$ and the other student estimates the area to be $150 \mathrm{~m}^{2}$ or less.

$\frac{3840}{10712}$ oe isw $\left[\frac{480}{1339}\right]$
M2 for $[2\times]\left(\frac{24}{104}\times\frac{80}{103}\right)$ oe, or M1 for $\frac{24}{104},\frac{80}{103}$ seen.

[Maximum number: 9]

(a)

Figure for Question (a) — CAIE IGCSE Mathematics Extended

The diagram shows 11 cards.

[ 4 ]

(i)

One of these cards is chosen at random.
Write down the probability that the letter on the card is not A.

[ 1 ]

$\frac9{11}$

(ii)

A card is chosen at random from these 11 cards and then replaced.
A second card is then chosen at random.
Find the probability that exactly one card has the letter N.

[ 3 ]

$\frac{36}{121}$ oe
M2 for $2\times\frac2{11}\times\frac9{11}$ oe
or M1 for $\frac2{11}\times\frac9{11}$ oe
If 0 scored, SC1 for $\frac{36}{110}$

(b)

Figure for Question (b) — 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.

[ 5 ]

(i)

A student is chosen at random.

Find the probability that this student likes English and likes mathematics.

[ 1 ]

$\frac{28}{50}$ oe
FT their 28 where their 28 < 50

(ii)

Two students are chosen at random.

Find the probability that they both like mathematics.

[ 2 ]

$\frac{123}{175}$ oe
M1 for $\frac{42}{50}\times\frac{41}{49}$

(iii)

Two students who like English are chosen at random.

Find the probability that they both also like mathematics.

[ 2 ]

$\frac{63}{88}$ oe
FT their 28
M1 for $\frac{\text{their }28}{33}\times\frac{\text{their }28-1}{32}$

[Maximum number: 6]

(a)

At a festival, 380 people out of 500 people questioned say that they are camping. There are 55300 people at the festival.

Calculate an estimate of the total number of people camping at the festival.

[ 2 ]

42028
M1 for $\frac{380}{500}$ oe soi isw

(b)

12 friends travel to the festival.

5 travel by car, 4 travel by bus and 3 travel by train.
Two people are chosen at random from the 12 friends.
Calculate the probability that they travel by different types of transport.

[ 4 ]

$\frac{47}{66}$ oe
0.712...
M3 for $2(\frac5{12}\times\frac4{11})+2(\frac4{12}\times\frac3{11})+2(\frac5{12}\times\frac3{11})$ oe
or $1-(\frac5{12}\times\frac4{11}+\frac4{12}\times\frac3{11}+\frac3{12}\times\frac2{11})$ oe
or M2 for sum of 3 or more correct product pairs and no incorrect pairs
M1 for $\frac{k}{12}\times\frac{j}{11}$ seen
If 0 scored, SC1 for $\frac{94}{144}$ oe

All question bank results loaded

Covered syllabus points

8. Probability question 1

8. Probability question 2

Question (a)

Question (i)

Question (ii)

Question (b)

Question (i)

Question (ii)

Question (iii)

8. Probability question 3

Question (a)

Question (b)