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  • Explain solution RD Sharma class 12 chapter Probability exercise 30.1 question 8 maths

Explain solution RD Sharma class 12 chapter Probability exercise 30.1 question 8 maths

Answers (1)

Answer:

\frac{5}{6},\frac{1}{2} 

Hint:

Use Formula

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

Given,

\begin{aligned} &P(A)=\frac{1}{3}\\ &P(B)=\frac{1}{5}\\ &P(A\cup B)=\frac{11}{30}\\ \end{aligned}

We know that,

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

\begin{aligned} &\frac{11}{30}=\frac{1}{3}+\frac{1}{5}-P(A\cap B)\\ &P(A\cap B)=\frac{8}{15}-\frac{11}{30}\\ &P(A\cap B)=\frac{16-11}{30}\\ &\qquad \qquad =\frac{5}{30}\\ &P(A\cap B)=\frac{1}{6} \end{aligned}

Now for,

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

Posted by

Gurleen Kaur

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