CAIE IGCSE Mathematics Extended E8.3.1 Calculate the Probability of Combined Events Using Where Appropriate Questions

Practise Extended CAIE IGCSE Mathematics by representing combined events, multiplying conditional branches, adding mutually exclusive cases, and applying complements.

Exam points

Represent combined events with sample-space, Venn or tree diagrams and identify the relevant outcomes.
Calculate combined-event probabilities by multiplying along independent or conditional branches and adding mutually exclusive cases.
Apply with- or without-replacement methods and complement reasoning to interpret combined probabilities in context.

[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.

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CAIE IGCSE Mathematics Extended E8.3.1 Calculate the Probability of Combined Events Using Where Appropriate Questions question 1

Question (a)

Question (b)