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ACT Exam  >  ACT Questions  >  A and B are two events such that P(B) = 0.4 a... Start Learning for Free
A and B are two events such that P(B) = 0.4 and P(A ∪ B) = 0.6 If A and B are independent, then P(A) is
  • a)
    1/2
  • b)
    1/3
  • c)
    2/3
  • d)
    2/5
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A and B are two events such that P(B) = 0.4 and P(A ∪ B) = 0.6 If ...
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 
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Most Upvoted Answer
A and B are two events such that P(B) = 0.4 and P(A ∪ B) = 0.6 If ...
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 
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A and B are two events such that P(B) = 0.4 and P(A ∪ B) = 0.6 If A and B are independent, then P(A) isa)1/2b)1/3c)2/3d)2/5Correct answer is option 'B'. Can you explain this answer?
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