CAIE A-Level Mathematics 5.3.4 Conditional Probability

Practise using tree diagrams and restricted sample spaces to calculate conditional probabilities in staged events.

[Maximum number: 2]

In the region of Arka, the total number of households in the three villages Reeta, Shan and Teber is 800 . Each of the households was asked about the quality of their broadband service. Their responses are summarised in the following table.

Table for Question 5.3.4—Elementary probability question 1 — CAIE A-Level Mathematics AS

Find the probability that a randomly chosen household has good broadband service given that the household is in Shan.

In the whole of Arka there are a large number of households. A survey showed that 35 % of households in Arka have no broadband service.

$\frac{177}{223+177+40}$
M1
Their 223+177+40 seen as denominator of fraction
in the final answer, accept unsimplified
$\frac{177}{440}$ or 0.402
A1
CAO
Alternative method for Question 7(a)(ii)
$\mathrm{P}(\mathrm{G} \mid \mathrm{S})=\frac{\mathrm{P}(G \cap S)}{\mathrm{P}(S)}=\frac{\frac{177}{800}}{\frac{223+177+40}{800}}=\frac{\frac{177}{800}}{\frac{440}{800}}=\frac{\frac{177}{800}}{\frac{11}{20} \text { or } 0.55}$
M1
Their \mathrm{P}(S) seen as denominator of fraction in the final
answer, accept unsimplified
$\frac{177}{440}$ or 0.402
A1
CAO

All question bank results loaded

5.3.4—Elementary probability question 1