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JEE Advanced2007MathematicsProbabilityActual

Let E^c denotes the complement of an event E . Let E, F, G be pairwise independent events with P(G)>0 and P(E F G)=0 . Then, P (E^c F^c G ) equals

Options

  1. AP (E^c )+P (F^c )
  2. BP (E^c )-P (F^c )
  3. CP (E^c )-P(F)
  4. DP(E)-P (F^c )

Correct answer

C. P (E^c )-P(F)

Step-by-step solution

aligned P ( E^c F^c G ) & = P (E^c F^c G ) P(G) & = P(G)-P(E G)-P(G F) P(G) & = P(G)[1-P(E)-P(F)] P(G) & =1-P(E)-P(F) & =P (E^c )-P(F) . aligned

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