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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Probability

NDA 2013 · Mathematics · Probability

If A and B are any two events such that P( A )=0.4 , P( B )=0.3,...

If AA and BB are any two events such that P(Aˉ)=0.4P(\bar{A})=0.4, P(B‾)=0.3,P(A∪B)=0.9\mathrm{P}(\overline{\mathrm{B}})=0.3, \mathrm{P}(\mathrm{A} \cup \mathrm{B})=0.9, then what is the value of P(A‾∪B‾)\mathrm{P}(\overline{\mathrm{A}} \cup \overline{\mathrm{B}}) equal to?

Options

  1. A0.20.2
  2. B0.50.5
  3. C0.60.6
  4. D0.70.7

Correct answer

C. 0.60.6

Step-by-step solution

P(A‾∪B‾)=P(A‾)+P(B‾)−P(A‾∩B‾)=P(A‾)+P(B‾)−P(A∪B‾)\begin{aligned} & \mathrm{P}(\overline{\mathrm{A}} \cup \overline{\mathrm{B}})=\mathrm{P}(\overline{\mathrm{A}})+\mathrm{P}(\overline{\mathrm{B}})-\mathrm{P}(\overline{\mathrm{A}} \cap \overline{\mathrm{B}}) \\ &=\mathrm{P}(\overline{\mathrm{A}})+\mathrm{P}(\overline{\mathrm{B}})-\mathrm{P}(\overline{\mathrm{A} \cup \mathrm{B}})\end{aligned}=\mathrm{P}(\overline{\mathrm{A}})+\mathrm{P}(\overline{\mathrm{B}})-(1-\mathrm{P}(\mathrm{A} \cup \mathrm{B}))=.4+.3-(1-.9)=.6$
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