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  • Provide Solution For R.D. Sharma Maths Class 12 Chapter 30 Probaility Exercise Multiple Choice Questions Question 32 Maths Textbook Solution.

Provide Solution For  R.D. Sharma Maths Class 12 Chapter 30 Probaility  Exercise Multiple Choice Questions Question 32 Maths Textbook Solution.

Answers (1)

Answer:(c)

Hint: You must know the rules of finding probability.

Given:P(A)=\frac{2}{5}, P(B)=\frac{3}{10}, P(A \cap B)=\frac{1}{5}

Solution:

\begin{aligned} &P(\bar{A})=1-P(A)=1-\frac{2}{5}=\frac{3}{5} \\\\ &P(\bar{B})=1-P(B)=1-\frac{3}{10}=\frac{7}{10} \\\\ &\therefore P(A \cup B)=P(A)+P(B)-P(A \cap B) \\ \end{aligned}

\begin{aligned} &=\frac{2}{5}+\frac{3}{10}-\frac{1}{5} \\\\ &=\frac{4+3-2}{10}=\frac{5}{10} \\\\ &=\frac{1}{2} \end{aligned}

Also,

\begin{aligned} &P\left(\frac{\bar{A}}{\bar{B}}\right) \times P\left(\frac{\bar{B}}{\bar{A}}\right)=\frac{P(\bar{A} \cap \bar{B})}{P(\bar{B})} \times \frac{P(\bar{A} \cap \bar{B})}{P(\bar{A})} \\\\ &=\frac{\left(\frac{1}{2}\right)}{\left(\frac{7}{10}\right)} \times \frac{\left(\frac{1}{2}\right)}{\left(\frac{3}{5}\right)}=\frac{10}{2 \times 7} \times \frac{5}{3 \times 2} \\\\ &=\frac{25}{42} \end{aligned}

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