CAIE IGCSE Mathematics Extended E8.3.1 Methods for Combined-Event Probability

Practise choosing sample spaces, Venn diagrams or tree diagrams for combined events with or without replacement.

Exam points

choose a tree, Venn diagram or sample space that represents the event structure
adjust second-stage counts and totals for selection without replacement
combine products or set regions to calculate intersection or union probabilities

[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 E8.3.1 Calculate the probability of combined events using, where appropriate: 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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E8.3.1 Calculate the probability of combined events using, where appropriate: question 1