Question

Assertion :If A & B are independent with probabilities $P\left(A\right)=\frac{1}{2},P\left(B\right)=\frac{1}{5}$ then $P(A\cup B)=\frac{3}{5}$ . Reason: For independent events A & B the result $P(A\cap B)=P\left(A\right)P\left(B\right)$ holds true.

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

For independent events $A$ & $B$

$P(A\cap B)=P\left(A\right)P\left(B\right)=\frac{1}{2}\times \frac{1}{5}=\frac{1}{10}$

Now $P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$=\frac{1}{2}+\frac{1}{5}-\frac{1}{10}=\frac{3}{5}$

Hence Assertion is followed by Reason.