CAIE IGCSE Mathematics Extended E8.3 Probability of Combined Events Question Bank

Practise multi-stage probability using trees, Venn diagrams and selections with or without replacement.

Exam points

update branch probabilities when a selection is made without replacement
multiply along a route and add all routes satisfying the required outcome
translate Venn or table regions into intersection and union probabilities

Covered syllabus points

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

[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 E8.3 Probability of combined events 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.

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Covered syllabus points

E8.3 Probability of combined events question 1