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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
MCQ
If $A$ and $B$ are two events, then $\text{P}(\overline{\text{A}}\cap\text{B})=$
  • A
    $\text{P}(\overline{\text{A}})\text{ P}(\overline{\text{B}})$
  • B
    $1-\text{P}(\text{A})-\text{P}(\text{B})$
  • C
    $\text{P}(\text{A})+\text{P}(\text{B})-\text{P}(\text{A}\cap\text{B})$
  • ✓
    $\text{P}(\text{B})-\text{P}(\text{A}\cap\text{B})$
✓

Answer

Correct option: D.
$\text{P}(\text{B})-\text{P}(\text{A}\cap\text{B})$

From the diagram, we get $\text{A}\cap\text{B}$ and $\overline{\text{A}}\cap\text{B}$ are mutually exclusive events such that $(\text{A}\cap\text{B})\cup(\overline{\text{A}}\cap\text{B})=\text{B}.$ therefore by
$\text{P}(\text{A}\cap\text{B})+\text{P}(\overline{\text{A}}\cap\text{B})=\text{P(B)}$
$\therefore\ \text{P}(\overline{\text{A}}\cap\text{B})=\text{P(B)}-\text{P}(\text{A}\cap\text{B})$

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