Question

Assertion :The probability that candidates A & B can solve the problem $\frac{1}{5}$, $\frac{2}{5}$, then probability that problem will be solved is given by $\frac{12}{25}$. Reason: If events A & B are independent, then $P(A\cap B)=P\left(A\right)\times P\left(B\right)$.

• A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
• B. Both Assertion & 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

Probability of solving the problem by $A$ & $B$ is
$=1-P$(None of them can solve the problem)
$=1-P(\overline{A}\cap \overline{B})$
$=1-P\left(\overline{A}\right)\cdot P\left(\overline{B}\right)$
$=1-[1-P\left(\overline{A}\right)][1-P\left(\overline{B}\right)]$
$=1-\frac{4}{5}\times \frac{3}{5}=\frac{13}{25}$

However the reason is true from the property of independent events.