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Probability — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsProbability2 Marks
Question
If A and B are two events associated with a random experiment such that $\text{P}(\text{A}\cup\text{B})=0.8,\ \text{P}(\text{A}\cap\text{B})=0.3$ and $\text{P}(\overline{\text{A}})=0.5,$ find P(B).
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Answer

We know,
$\text{P}(\text{A}\cup\text{B})=0.8$
$\text{P}(\text{A}\cap\text{B})=0.3$
$\text{P}(\overline{\text{A}})=0.5$
$\Rightarrow1-\text{P}({\text{A}})=0.5$
$\Rightarrow\text{P}({\text{A}})=1-0.5=0.5$
Now, by adding theorem on probability
$\text{P}(\text{A}\cup\text{B})=\text{P}(\text{A})+\text{P}(\text{B})-\text{P}(\text{A}\cap\text{B})$
$0.8=0.5+\text{P}(\text{B})-0.3$
$0.8=\text{P}(\text{B})+0.2$
$\text{P}(\text{B})=0.8-0.2$
$=0.6$
$\therefore\text{P}(\text{B})=0.6$

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