Let two that conditional probabilities Then | Probability...

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JEE MAIN 2022

25-6-2022 S1

Question

Let $E_1$ and $E_2$ be two events such that the conditional probabilities $P\left(E_1 \mid E_2\right)=\frac{1}{2}, P\left(E_2 \mid E_1\right)=\frac{3}{4}$ and $P\left(E_1 \cap E_2\right)=\frac{1}{8}$. Then :

Select the correct option:

A

$P\left(E_1 \cap E_2\right)=P\left(E_1\right) \cdot P\left(E_2\right)$

B

$P\left(E_1^{\prime} \cap E_2^{\prime}\right)=P\left(E_1^{\prime}\right) . P\left(E_2\right)$

C

$P\left(E_1 \cap E_2^{\prime}\right)=P\left(E_1\right)_{\ldots \dot{m}} P\left(E_2\right)$

D

$P\left(E_1^{\prime} \cap E_2\right)=P\left(E_1\right) . P\left(E_2\right)$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

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