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

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_53 Year：2021 Question No：7(a)(ii)

Answer:

\(
\begin{array}{l}
\frac{177}{223+177+40} \\
\frac{177}{440} \text { or } 0.402
\end{array}
\)
Alternative method for Question 7(a)(ii)
\[
P(\mathrm{G} \mid \mathrm{S})=\frac{P(G \cap S)}{P(S)}=\frac{\frac{177}{800}}{\frac{223+177+40}{800}}=\frac{\frac{177}{800}}{\frac{440}{800}}=\frac{\frac{177}{800}}{\frac{11}{20} \text { or } 0.55}
\]
\(\frac{177}{440}\) or \(0.402\)

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