If A and B are two independent events, then A and bar B are

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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

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