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Probability — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsProbability2 Marks
Question
If $\mathrm{P}\left(\mathrm{A}^{\prime}\right)=0.7, \mathrm{P}(\mathrm{B})=0.7, \mathrm{P}(\mathrm{B} / \mathrm{A})=$ 0.5 , find $\mathrm{P}(\mathrm{A} / \mathrm{B})$ and $\mathrm{P}(\mathrm{A} \cup \mathrm{B})$.
✓

Answer

Since $1-P\left(A^{\prime}\right)=0.7$
$
\mathrm{P}(\mathrm{A})=1-\mathrm{P}\left(\mathrm{A}^{\prime}\right)=1-0.7=0.3
$
Now $\mathrm{P}(\mathrm{B} / \mathrm{A})=\mathrm{P}(\mathrm{A} \cap \mathrm{B}) / \mathrm{P}(\mathrm{A})$
$
\therefore 0.5=\mathrm{P}(\mathrm{A} \cap \mathrm{B}) / 0.3
$
$\therefore \mathrm{P}(\mathrm{A} \cap \mathrm{B})=0.15$
Again $\mathrm{P}(\mathrm{A} / \mathrm{B})=\mathrm{P}(\mathrm{A} \cap \mathrm{B}) / \mathrm{P}(\mathrm{B})$
$=0.15 / 0.7$
$\therefore \mathrm{P}(\mathrm{A} / \mathrm{B})=3 / 14$
Further, by addition theorem
$
\begin{aligned}
& P(A \cup B)=P(A)+P(B)-P(A \cap B) \\
& =0.3+0.7-0.15=0.85
\end{aligned}
$

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