Question:
If \(A\) and \(B\) are independent random variables, then which of the following is correct?
If \(A\) and \(B\) are independent random variables, then which of the following is correct?
Show Hint
If \(A\) and \(B\) are independent,
\[
\boxed{
P(A\mid B)=P(A),\qquad
P(A^c\mid B)=P(A^c).
}
\]
Updated On: Jul 23, 2026
- \(P(A^c\mid B)=P(A^c)\)
- \(P(A\mid B)=P(B)\)
- \(P(A\cup B)=P(A)\,P(B)\)
- \(P(A^c\cup B^c)=P(A^c)+P(B^c)\)
Show Solution
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The Correct Option is A
Solution and Explanation
For independent events,
\[
P(A\mid B)=P(A).
\]
The complement of an independent event is also independent.
Hence,
\[
P(A^c\mid B)=P(A^c).
\]
Therefore,
\[
\boxed{(A)}
\]
is correct.
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