Correct Answer - Option 2 :
\(\frac 13\)
Concept:
Independent events:
Two events are independent if the incidence of one event does not affect the probability of the other event.
If A and B are two independent events, then P(A ∩ B) = P(A) × P(B)
Calculation:
Given: P(B) = 0.4 and P(A ∪ B) = 0.6
P(A ∪ B) = 0.6
⇒ P(A) + P(B) - P(A ∩ B) = 0.6
⇒ P(A) + P(B) - P(A) × P(B) = 0.6 (∵ A and B are independent events.)
⇒ P(B) + P(A) [1 - P(B)] = 0.6
⇒ 0.4 + P(A) [1 - 0.4] = 0.6
⇒ P(A) × 0.6 = 0.2
\(\therefore {\rm{P}}\left( {\rm{A}} \right) = \frac{{0.2}}{{0.6}} = \frac{1}{3}\)
