CAIE IGCSE Mathematics Extended 8 Probability

Covered syllabus points

E8.1 Introduction to probability E8.2 Relative and expected frequencies E8.3 Probability of combined events E8.4 Conditional probability

[Maximum number: 5]

On any day the probability that it rains is $\frac{1}{3}$ .
When it rains the probability that Amira goes fishing is $\frac{3}{5}$ .
When it does not rain the probability that Amira goes fishing is $\frac{3}{4}$ .

(a)

Complete the tree diagram.

Figure for Question (a) — CAIE IGCSE Mathematics Extended

[ 2 ]

Figure for Answer to Question (a) — CAIE IGCSE Mathematics Extended

$\frac{2}{3},\frac{2}{5},\frac{3}{4},\frac{1}{4}$ oe

M1 for 2 or 3 correct.

(b)

Find the probability that on any day Amira goes fishing.

[ 3 ]

$\frac{7}{10}$ oe

M2 for $\frac13\times\frac35+$ their $\frac23\times$ their $\frac34$ .
M1 for one product.

[Maximum number: 4]

Dice A

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.

(a)

Dice A and Dice B are each rolled once.

[ 2 ]

(i)

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

[ 2 ]

$\frac2{11}$ oe
M1 for $\frac2k$ or $\frac{p}{\text{their }11}$ seen oe leading to answer

(b)

Dice B is rolled n times.

The probability that on the nth roll it first lands on a number 3 is 32/729.
Find the value of n.

n=

[ 2 ]

6
M1 for $\left(\frac46\right)^k\times\frac26=\frac{32}{729}$ written oe, soi by one trial with k>1, or $2^{n-1}=32$ or better, or $3^n=729$ or better

[Maximum number: 8]

A bag contains 5 red balls, 4 blue balls and 3 green balls.

(a)

Megan picks a ball at random.
Write down the probability that the ball is red or blue.

[ 1 ]

$\frac34$ oe

(b)

Megan replaces the ball.
She picks a ball at random, notes the colour and replaces the ball.
She repeats this 60 times.
Calculate the number of times the ball is expected to be red or blue.

[ 1 ]

45
FT $60\times$ their (a)(i) correctly evaluated

(c)

Mick picks 2 of the 12 balls at random, without replacement.
Calculate the probability that the balls are different colours.

[ 4 ]

$\frac{47}{66}$ oe
M3 for $1-\left(\frac5{12}\times\frac4{11}+\frac4{12}\times\frac3{11}+\frac3{12}\times\frac2{11}\right)$ oe
or M2 for the complementary same-colour sum or different-colour sum
or M1 for one correct product term
If 0 scored, SC1 for $\frac{47}{72}$ oe

(d)

Marie picks balls at random, without replacement, from the 12 balls.
When she picks a green ball she stops.
The probability that she picks a green ball on pick n is $\frac{21}{220}$ .
Find the value of n.
n=

[ 2 ]

[Maximum number: 4]

Table for Question 4 — CAIE IGCSE Mathematics Extended

The table shows information about the heights of 80 children.

(a)

One of these children is chosen at random.

Calculate the probability that they have a height of 1.4 m or less.

[ 1 ]

$\frac{1}{40}$ oe

1

(b)

Two of these children are chosen at random.

Calculate the probability that both children are taller than 1.5 m but only one of them is taller than 1.8 m .

[ 3 ]

$\frac{63}{395}$ oe
M2 for $\frac{56}{80}\times\frac9{79}\times2$ oe, or B1 for $\frac{56}{80}$ , $\frac9{79}$ , $\frac9{80}$ or $\frac{56}{79}$ seen
If 0 or B1 scored, SC2 for $\frac{117}{632}$ oe or SC1 for $\frac{63}{400}$ oe

All question bank results loaded

CAIE IGCSE Mathematics Extended 8 Probability Topic Practice

Covered syllabus points

Question 1

Question (a)

Question (b)

Question 2

Question (a)

Question (i)

Question (b)

Question 3

Question (a)

Question (b)

Question (c)

Question (d)

Question 4

Question (a)

Question (b)