Question

Assertion :A and B are two candidates seeking in D.C. E. The probability that A is selected is 0.40 & the probability that both A and B are selected is 0.20. Then the probability of B's selection is 0.60. Reason: If $E_1$ and $E_2$ are the events of selection of A and B respectively, then $P(E_1\cap E_2)=P\left(E_1\right)P\left(E_2\right)$.

• A. Both Assertion and Reason are individually true and Reason is correct explanation of Assertion
• B. Both Assertion and Reason are individually true but Reason is not the correct (proper) explanation of Assertion
• C. Assertion is true but Reason is false
• D. Assertion is false but Reason is true

Answer 1

The correct option is D Assertion is false but Reason is true

By Assertion $P(E_1\cap E_2)\le 0.20$
$P\left(E_1\right)\cdot P\left(E_2\right)\le 0.20\Rightarrow \left(0.40\right)P\left(E_2\right)\le 0.20$
$\therefore P\left(E_2\right)\le \frac{2}{4}=\frac{1}{2}=0.5$
Thus $P\left(E_2\right)$ can't be $0.6$

Or the probability of $B^{\prime }s$ selection is not 0.60
Hence Assertion (A) is false & Reason (R) is true.