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Most Important Selected Qs for JEE AdvancedMathematicsProbability

Events A and B satisfy P(A)=0.4, P(B)=0.5 and P(A B)=0.8 . Which of the following statement (s) is/are CORRECT?

Options

  1. AP ( A B )= 2 5
  2. BP ( B / A )= 2 3
  3. CP ( A B ) P ( A ) P ( B )
  4. DP( exactly one of either A or B occurs )= 7 10

Correct answer

D. P( exactly one of either A or B occurs )= 7 10

Step-by-step solution

aligned & P ( ~A )+ P ( ~B )- P ( ~A ~B )=0.8 & P ( ~A ~B )=0.5+0.4-0.8=0.1 & P ( ~A ~B )= P ( ~B )- P ( ~A ~B ) & =0.5-0.1=0.4 ( ~A ) is correct & P ( ~B / A )= P ( ~B ~A ) P ( ~A ) = 0.4 1- P ( ~A ) = 0.4 0.6 = 2 3 aligned (B) is correct aligned & P ( ~A ) P ( ~B )=0.2 & P ( ~A ~B ) P ( ~A ) P ( ~B ) & ( C ) is correct & P ( ~A or B but not both )=0.9-2 0.1=0.7 aligned

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