A) \[P(B/A)=P(B)-P(A)\]
B) \[P({{A}^{c}}\cup {{B}^{c}})=P({{A}^{c}})+P({{B}^{c}})\]
C) \[P{{(A\cup B)}^{c}}=P({{A}^{c}})P({{B}^{c}})\]
D) \[P(A/B)=P(A)+P({{B}^{c}})\]
Correct Answer: C
Solution :
Since,\[P(A\cap B)=P(A)P(B)\] \[\Rightarrow \]A and B are independent events \[\Rightarrow \]\[{{A}^{c}}\]and\[{{B}^{c}}\]will also indent events Hence, \[P{{(A\cup B)}^{c}}=P({{A}^{c}}\cap {{B}^{c}})\] \[=P({{A}^{c}})\cap P({{B}^{c}})\] \[\therefore \]Option (c) is correct. Note: If two events A and B are independent, then its complement is also independent.
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