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A and B are independent events. P(A|B) = 0.4. Find P(A).
Round your answer to the nearest tenth.
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By the definition of the conditional probability,
P(A|B) = . (1)
By the definition, the events A and B are independent if
P(A and B) = P(A)*P(B). (2)
By substituting (2) into (1), you have
P(A|B) = = P(A).
But P(A|B) is given: it is 0.4.
Therefore, at given conditions, P(A) = 0.4. ANSWER.
Solved.
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This result justifies the name of independent events:
for independent events A and B, P(A|B) does not depend on P(B) and is equal to P(A).