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  • Provide solution for RD Sharma Maths Class 12 Chapter 30 Probability Exercise 30.3 question 7.

Provide solution for RD Sharma Maths Class 12 Chapter 30 Probability Exercise 30.3 question 7.

Answers (1)

Answer: \frac{4}{11},\frac{4}{5},\frac{2}{3}

Hint: Use \Rightarrow P(A \cup B)=P(A)+P(B)-P(A \cap B) 

Given,

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

Solution:

Now, (i)

 \begin{aligned} &P(A \cup B)=P(A)+P(B)-P(A \cap B) \\ &\frac{7}{11}=\frac{6}{11}+\frac{5}{11}-P(A \cap B) \\ &P(A \cap B)=1-\frac{7}{11} \\ &P(A \cap B)=\frac{4}{11} \end{aligned}               

               

(ii) 

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

(iii)

\begin{aligned} &P(B \mid A)=\frac{P(A \cap B)}{P(A)} \\ &=\frac{\frac{4}{11}}{\frac{6}{11}} \\ &=\frac{4}{6}=\frac{2}{3} \end{aligned}

     

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