Let A and B be two events such that $P(A) = 0.3 $ and $P(A ∪ B)=0.8$. If A and B are independent events, then P(B)=
Answer & explanation
Correct answer: option 2
Here $P(A ∪ B)=0.8, P(A) = 0.3 $ and A and B are independent events.
Let P(B) = x
$∴ P(A ∪ B)= P(A) + P(B) - P(A ∩ B)⇒ P(A ∪ B)= P(A) +P(B) - P(A).P(B)$
$⇒ 0.8 = 0.3 + x - 0.3 x ⇒ x =\frac{5}{7}.$