Question

Assertion :If $P\left(A\right)=0\cdot 3$ and $P(A\cup \overline{B})=0\cdot 8$, then P(B) is $\frac{2}{7}$. Reason: $P\left(\overline{E}\right)=1-P\left(E\right)$, where E is any event.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$P\left(A\right)=0\cdot 3$
$P(A\cup \overline{B})=0\cdot 8$
$P(A\cup \overline{B})=P\left(A\right)+P\left(\overline{B}\right)-P(A\cap \overline{B})$
$P(A\cup \overline{B})=P\left(A\right)+1-P\left(B\right)-P\left(A\right)(1-P(B\left)\right)$
$0\cdot 8=0\cdot 3+1-P\left(B\right)-0\cdot 3+0\cdot 3P\left(B\right)$
$0\cdot 2=0\cdot 7P\left(B\right)$
$P\left(B\right)=\frac{2}{7}$