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  • Provide solution for RD Sharma Maths Class 12 Chapter 30 Probability Exercise 30.3 question 5 sub question (ii).

Provide solution for RD Sharma Maths Class 12 Chapter 30 Probability Exercise 30.3 question 5 sub question (ii).

Answers (1)

Answer: \frac{4}{5},\frac{2}{3}

Hint:

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

Solution:

Given,

\begin{aligned} &P(A)=\frac{6}{11} \\ &P(B)=\frac{5}{11} \\ &P(A \cup B)=\frac{7}{11} \end{aligned}

Now,

\begin{aligned} &P(A \mid B)=\frac{P(A \cap B)}{P(B)} \\ &=\frac{\frac{4}{11}}{\frac{5}{11}} \\ &=\frac{4}{5} \end{aligned}

\begin{aligned} P(B \mid A) &=\frac{P(A \cap B)}{P(A)} \\ &=\frac{\frac{4}{11}}{\frac{6}{11}} \end{aligned}

                    =\frac{4}{6} =\frac{2}{3}

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