Let A and B be independent events with P(A) = 1/4 and P(A ∪ B) = 2P(B) - P(A). Find P(B)

Question

Let A and B be independent events with P(A) = 1/4 and P(A ∪ B) = 2P(B) - P(A). Find P(B) (A) (1/4) (B) (3/5) (C) (2/3) (D) (2/5)

Tardigrade Admin · Accepted Answer

We know that, P(A ∪ B ) = P(A) + P(B) - P(A ∩ B) = P(A) + P(B) - P(A) P(B) (Since A, B are independent) Thus, we know that 1/4 + P(B) - (1/4) P(B) = 2P(B) - 1/4, implying that P(B) = 2/5.

Q. Let $A$ and $B$ be independent events with $P (A) = 1/4$ and $P (A \cup B) = 2 P (B) - P (A)$ . Find $P (B)$

$\frac{1}{4}$

$\frac{3}{5}$

$\frac{2}{3}$

$\frac{2}{5}$

We know that,
$P (A \cup B) = P (A) + P (B) - P (A \cap B)$
$= P (A) + P (B) - P (A) P (B)$
(Since $A$ , $B$ are independent)
Thus, we know that
$1/4 + P (B) - (1/4) P (B) = 2 P (B) - 1/4$ , implying that $P (B) = 2/5$ .

Q. Let A and B be independent events with P(A)=1/4 and P(A∪B)=2P(B)−P(A). Find P(B)

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