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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
MCQ
Choose the correct answer from the given four options:If $A$ and $B$ are such events that $\text{P}(\text{A})>0$ and $\text{P}(\text{B})\neq1,$ then $\text{P}\Big(\frac{\text{A}'}{\text{B}'}\Big)$ equals to:
  • A
    $1-\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)$
  • B
    $1-\text{P}\Big(\frac{\text{A}'}{\text{B}}\Big)$
  • ✓
    $\frac{1-\text{P}(\text{A}\cup\text{B})}{\text{P}(\text{B}')}$
  • D
    $\frac{\text{P}(\text{A}')}{\text{P}(\text{B}')}$
✓

Answer

Correct option: C.
$\frac{1-\text{P}(\text{A}\cup\text{B})}{\text{P}(\text{B}')}$
We have, $\text{P}(\text{A})>0$ and $\text{P}(\text{B})\neq1$
$\text{P}\Big(\frac{\text{A}'}{\text{B}'}\Big)=\frac{\text{P}(\text{A}'\cap\text{B}')}{\text{P}(\text{B}')}$
$=\frac{1-\text{P}(\text{A}\cup\text{B})}{\text{P}(\text{B}')}$

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