MHT CET · Maths · Probability
If \(P\left(A^{\prime}\right)=0 \cdot 6, P(B)=0 \cdot 8\) and \(P(B / A)=0 \cdot 3\), then \(P(A / B)=\)
- A \(\frac{7}{20}\)
- B \(\frac{3}{20}\)
- C \(\frac{3}{4}\)
- D \(\frac{9}{20}\)
Answer & Solution
Correct Answer
(B) \(\frac{3}{20}\)
Step-by-step Solution
Detailed explanation
Given \(P\left(A^{\prime}\right)=0.6 \Rightarrow P(A)=1-0.6=0.4, P(B)=0.8,\) \(P(B / A)=0.3\)
We know that \(\mathrm{P}(\mathrm{B} / \mathrm{A})=\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{A})}\) and \(\mathrm{P}(\mathrm{A} / \mathrm{B})=\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{B})}\)
Here \(P(A \cap B)=P(A) \cdot P(B / A)=(0.4)(0.3)=0.12\)
Also \(\quad P(A \cap B)=P(A / B) \cdot P(B)\)
\(\therefore \mathrm{P}(\mathrm{A} / \mathrm{B})=\frac{0.12}{0.8}=\frac{12}{80}=\frac{3}{20}\)
We know that \(\mathrm{P}(\mathrm{B} / \mathrm{A})=\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{A})}\) and \(\mathrm{P}(\mathrm{A} / \mathrm{B})=\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{B})}\)
Here \(P(A \cap B)=P(A) \cdot P(B / A)=(0.4)(0.3)=0.12\)
Also \(\quad P(A \cap B)=P(A / B) \cdot P(B)\)
\(\therefore \mathrm{P}(\mathrm{A} / \mathrm{B})=\frac{0.12}{0.8}=\frac{12}{80}=\frac{3}{20}\)
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