JEE MAIN - Mathematics Hindi (2022 - 25th June Morning Shift - No. 7)
माना दो घटनाएँ $$\mathrm{E}_{1}$$ तथा $$\mathrm{E}_{2}$$ इस प्रकार है कि सप्रतिबंध प्रायिकताएँ $$\mathrm{P}^{2}\left(\mathrm{E}_{1} \mid \mathrm{E}_{2}\right)=\frac{1}{2}, \mathrm{P}\left(\mathrm{E}_{2} \mid \mathrm{E}_{1}\right)=\frac{3}{4}$$ तथा $$\mathrm{P}\left(\mathrm{E}_{1} \cap \mathrm{E}_{2}\right)=\frac{1}{8}$$ है। तो :
$$P\left(E_{1} \cap E_{2}\right)=P\left(E_{1}\right) \cdot P\left(E_{2}\right)$$
$$\mathrm{P}\left(\mathrm{E}_{1}^{\prime} \cap \mathrm{E}_{2}^{\prime}\right)=\mathrm{P}\left(\mathrm{E}_{1}^{\prime}\right) \cdot \mathrm{P}\left(\mathrm{E}_{2}\right)$$
$$\mathrm{P}\left(\mathrm{E}_{1} \cap \mathrm{E}_{2}^{\prime}\right)=\mathrm{P}\left(\mathrm{E}_{1}\right) \cdot \mathrm{P}\left(\mathrm{E}_{2}\right)$$
$$\mathrm{P}\left(\mathrm{E}_{1}^{\prime} \cap \mathrm{E}_{2}\right)=\mathrm{P}\left(\mathrm{E}_{1}\right) \cdot \mathrm{P}\left(\mathrm{E}_{2}\right)$$
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