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  • Provide solution for RD Sharma Maths Class 12 Chapter 30 Probability Exercise Case Study Based  Question, question 3 sub question (iii).

Provide solution for RD Sharma Maths Class 12 Chapter 30 Probability Exercise Case Study Based  Question, question 3 sub question (iii).

Answers (1)

Answer:

            (d)

Hint:

            You must know rules of conditional probability

Given:

            90% test detect the disease, 10% go undetected, 99% judged HIV –ve and 1% judged

HIV +ve, 0.1% have HIV

Solution:

Let the events be,

E=Person selected has HIV

F=Person selected does not have HIV

G=Test judges HIV +ve

\begin{aligned} &P(G)=P(E) \cdot P\left(\frac{G}{E}\right)+P(F) \cdot P\left(\frac{G}{F}\right) \\ &=0.001 \times 0.9+0.999 \times 0.01 \\ &=9 \times 10^{-4}+99.9 \times 10^{-4} \\ &=\frac{9+99.9}{10^{4}} \\ &=\frac{108.9}{10^{4}} \\ &=\frac{1089}{10^{5}} \\ &=0.01089 \end{aligned}

So, (d) is correct answer

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