A) \[P(1)-P({{B}^{c}})\]
B) \[P({{A}^{c}})+P({{B}^{c}})\]
C) \[P({{A}^{c}})-P({{B}^{c}})\]
D) \[P({{A}^{c}})-P(B)\]
Correct Answer: D
Solution :
\[P({{A}^{c}}\cap {{B}^{c}}/C)=\frac{P(({{A}^{c}}\cap {{B}^{c}})\cap C)}{P(C)}\] \[=\frac{P(C)-P(A\cap C)-P(B\cap C)+P(A\cap B\cap C)}{P(C)}\] \[=\frac{P(C)-P(A).P(C)-P(B)P(C)+0}{P(C)}\] \[=1-P(A)-P(B)\] \[=P({{A}^{c}})-P(B)\]
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