Explain solution RD Sharma class 12 chapter Probability exercise 30.7 question 28 maths

Answers (1)

Answer:

 \frac{14}{29}

Hint:

 Use Baye’s theorem.

Given:

 Assume that chance of patient having a heart attack is 40%. If is also assumed that meditation and yoga source reduce the rest of heart attack by 30% and preparation of certain drug reduce its chance by 25%.

Solution:

Let A1,E1 and E2  denote event that person has heart attack, the selected person followed the source of yoga and meditation and person adopt drug precaution.

\begin{aligned} &P(A)=0.40\\ &P(E_1)=P(E_2)=\frac{1}{2}\\ &P\left ( \frac{A}{E_1} \right )=0.28=(0.40\times 0.70)\\ &P\left ( \frac{A}{E_2} \right )=0.40\times 0.75=0.30\\ \end{aligned}

Using Baye’s theorem we get

\begin{aligned} &P\left (\frac{E_1}{A} \right )=\frac{P(E_1).P\left ( \frac{A}{E_1} \right )}{P(E_1)\times P\left ( \frac{A}{E_1} \right )+P(E_2)\times P\left ( \frac{A}{E_2} \right )}\\ &=\frac{{\frac{1}{2}\times 0.28 }}{\frac{1}{2}\times 0.28+\frac{1}{2}\times 0.30}\\ &=\frac{14}{29} \end{aligned}

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