CAIE IGCSE Mathematics Extended E8.3 Probab…vents

Covered syllabus points

E8.3.1 Calculate the probability of combined events using, where appropriate:

[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]

A bag contains 2 green buttons, 5 red buttons and 6 blue buttons. Two buttons are taken at random from the bag without replacement.

Calculate the probability that the two buttons are different colours.

$\frac23$ oe nfww
M3 for $\frac2{13}\times\frac{11}{12}+\frac5{13}\times\frac8{12}+\frac6{13}\times\frac7{12}$ oe
or $1-\left(\frac2{13}\times\frac1{12}+\frac5{13}\times\frac4{12}+\frac6{13}\times\frac5{12}\right)$ oe
or M2 for sum of three or more correct product pairs and no incorrect pairs

[Maximum number: 2]

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.

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=

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

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CAIE IGCSE Mathematics Extended E8.3 Probability of Combined Events Topic Practice

Covered syllabus points

Question 1

Question (a)

Question (b)

Question 2

Question 3