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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
If events $A$ and $B$ are independent, then identify the correct statements
(A) $A$ and $B$ must be mutually exclusive
(B) The sum of their probabilities must be equal to $1$
(C) $P(A)\cdot P(B) = P(A\cap B)$
(D) $A'$ and $B'$ are also independent
Choose the correct answer from the options given below:
Solution
For independent events
$P(A\cap B)=P(A)P(B)$
So statement (C) is **true**.
Independent events need not be mutually exclusive.
Therefore (A) is **false**.
Also $P(A)+P(B)$ need not be $1$.
Hence (B) is **false**.
If $A$ and $B$ are independent then their complements $A'$ and $B'$ are also independent.
Hence (D) is **true**.
Correct statements: **C and D**
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