14.Probability
medium

यदि $A$ और $B$ स्वतंत्र घटनाएँ हैं तो $A$ या $B$ में से न्यूनतम एक के होने की प्रायिकता $=1- P \left( A ^{\prime}\right) P \left( B ^{\prime}\right)$

Option A
Option B
Option C
Option D

Solution

We have

$P($  at least one of $A $ and $ B)=P(A \cup B)$

$=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})$

$=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B}$

$=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})[1-\mathrm{P}(\mathrm{A})]$

$=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B}) . \mathrm{P}\left(\mathrm{A}^{\prime}\right)$

$=1-\mathrm{P}\left(\mathrm{A}^{\prime}\right)+\mathrm{P}(\mathrm{B}) \mathrm{P}\left(\mathrm{A}^{\prime}\right)$

$=1-P\left(A^{\prime}\right)[1-P(B)]$

$=1-P\left(A^{\prime}\right) P\left(B^{\prime}\right)$

Standard 11
Mathematics

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