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14.Probability
easy
If $A$ and $B$ are two independent events, then $A$ and $\bar B$ are
A
Not independent
B
Also independent
C
Mutually exclusive
D
None of these
Solution
(b) Since $A \cap \bar B$ and $A \cap B$ are mutually exclusive events such that
$A = (A \cap \bar B) \cup (A \cap B)$
$\therefore$ $P(A) = P(A \cap \bar B) + P(A \cap B)$
$ \Rightarrow P(A \cap \bar B) = P(A) – P(A \cap B)$$ = P(A) – P(A)P(B)$
$( \because \, A,B$ are independent)
$ \Rightarrow P(A \cap \bar B)$$ = P(A)(1 – P(B)) = P(A)P(\bar B)$
$\therefore \,\,\,A$ and $\bar B$ are also independent.
Standard 11
Mathematics
