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Provide Solution For  R.D. Sharma Maths Class 12 Chapter 30 Probaility  Exercise Multiple Choice Questions Question 29 Maths Textbook Solution.

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Answer: (b)

Hint: You must know the rules of finding probability.

Given: \begin{aligned} &P(A \cup B)=\frac{4}{5^{\prime}} P(B)=\frac{3}{5}, P\left(\frac{A}{B}\right)=\frac{1}{2} \\ \end{aligned}

Solution:\begin{aligned} &P(B)=\frac{3}{5}, P\left(\frac{A}{B}\right)=\frac{1}{2} \end{aligned}

\begin{aligned} &\frac{P(A \cap B)}{P(B)}=\frac{1}{2} \\ &P(A \cap B)=\frac{1}{2} \times \frac{3}{5} \\ &P(A \cap B)=\frac{3}{10} \end{aligned}

Now,

\begin{aligned} &P(A \cup B)=\frac{4}{5} \\ &P(A)+P(B)-P(A \cap B)=\frac{4}{5} \\ \end{aligned}

\begin{aligned} &P(A)+\frac{3}{5}-\frac{3}{10}=\frac{4}{5} \\\\ &P(A)=\frac{4}{5}+\frac{3}{10}-\frac{3}{5} \\\\ &P(A)=\frac{8+3-6}{10} \\\\ &P(A)=\frac{5}{10}=\frac{1}{2} \end{aligned}

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