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AP EAMCET202123 Aug 2021Evening ShiftMathematicsProbabilityActual

Let A and B be events with P(A)= 1 3 , P(B)= 1 4 and P(A B)= 1 2 . Then Which of the following statements is incorrect?

Options

  1. AA and B are independent
  2. BP ( A B )= 1 3
  3. CP (A^C B )= 1 3
  4. DP (A B^C )= 1 4

Correct answer

C. P (A^C B )= 1 3

Step-by-step solution

Given, P(A)= 1 3 , P(B)= 1 4 , P(A B)= 1 2 P (A^C )=1-P(A)=1- 1 3 = 2 3 P(A) P(B)= 1 3 1 4 = 1 12 and P(A B)=P(A)+P(B)-P(A B)= 1 3 + 1 4 - 1 2 = 1 12 A and B are independent. aligned P(A / B) & = P(A B) P(B) = 1 / 12 1 / 4 =1 / 3 P (A^C B ) & =P(B)-P(A B) aligned = 1 4 - 1 12 = 1 6 P (A B^C )=P(A) P (B^C )= 1 3 (1- 1 4 )= 1 3 3 4 =1 / 4 P (A^C B )=1 / 3 is incorrect among above options.

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