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  • Provide solution for RD Sharma Maths Class 12 Chapter 30 Probability Exercise 30.3 question 5 sub question 1.

Provide solution for RD Sharma Maths Class 12 Chapter 30 Probability Exercise 30.3 question 5 sub question 1.

Answers (1)

Answer: \frac{2}{3},\frac{1}{2}

Hint:

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

Given,

\begin{aligned} &P(A)=\frac{1}{3} \\ &P(B)=\frac{1}{4} \\ &P(A \cup B)=\frac{5}{12} \end{aligned}

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

\begin{aligned} &P(A \cap B)=\frac{1}{3}+\frac{1}{4}-\frac{5}{12} \\ &P(A \cap B)=\frac{2}{12} \\ &P(A \cap B)=\frac{1}{6} \end{aligned} 

Solution:

Now,

\begin{gathered} P(A \mid B)=\frac{P(A \cap B)}{p(B)} \\ =\frac{\frac{1}{6}}{\frac{1}{4}} \\ =\frac{4}{6}=\frac{2}{3} \end{gathered}

\begin{gathered} P(B \mid A)=\frac{P(A \cap B)}{P(A)} \\ =\frac{\frac{1}{6}}{\frac{1}{3}} \\ =\frac{1}{2} \end{gathered}  

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