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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability3 Marks
Question
If P(A) = 0.4, P(B) = 0.3 and $\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)=0.5$ find $\text{P}(\text{A}\cap\text{B})$ and $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big).$
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Answer

Given,
P(A) = 0.4, P(B) = 0.3 and $\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)=0.5$
We know that,
$\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)=\frac{\text{P}(\text{A}\cap\text{B})}{\text{P(A)}}$
$=0.5=\frac{\text{P}(\text{A}\cap\text{B})}{0.4}$
$\text{P}(\text{A}\cap\text{B})=0.2$
$\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\frac{\text{P}(\text{A}\cap\text{B})}{\text{P(B)}}$
$=\frac{0.2}{0.3}$
$\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\frac{2}{3}$

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