Let A and B be two events. Suppose P(A) = 0.4, P(B) = p, and P(A⋃B) = 0.7. The value of p for which A and B are independent is

Engineering

Mathematics

Basic Definitions Related to Probability

Question

$\frac{1}{5}$

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{1}{3}$

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Given, P(A) = 0.4, P(B) = p, and P(A⋃B) = 0.7
A and B are independent events.
⇒ P(A U B) = P(A) + P(B) − P(A) × P(B)

0.7 = 0.4 + p − 0.4p
$p = \frac{1}{2}$