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

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

Answers (1)

Answer:

            (c)

Hint:

            You must know rules of conditionalprobability

Given:

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

HIV +ve, 0.1% have HIV

Solution:

E= Person selected has HIV

F= Person selected does not have HIV

G= Test judges HIV +ve

\begin{aligned} &P(E)=0.001 \\ &P(F)=0.999 \\ &P\left(\frac{G}{E}\right)=0.9 \\ &P\left(\frac{G}{F}\right)=0.01 \end{aligned}

We need to find the probability that person selected actually has HIV

Using baye’s theorem,

\begin{aligned} &P\left(\frac{E}{G}\right)=\frac{P(E) \cdot P\left(\frac{G}{E}\right)}{P(E) \cdot P\left(\frac{G}{E}\right)+P(F) \cdot P\left(\frac{G}{F}\right)} \\ &=\frac{0.001 \times 0.9}{0.001 \times 0.9+0.999 \times 0.01} \\ &=\frac{9 \times 10^{-4}}{9 \times 10^{-4}+99.9 \times 10^{-4}} \\ &=\frac{10^{-4} \times 9}{10^{-4}(9+99.9)} \\ &=\frac{9}{108.9}=\frac{90}{1089} \end{aligned}

So, (c) is correct answer

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