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KCET2022MathematicsProbability

If A and B are two events such that P(A)= 1 2 , P(B)= 1 2 and P(A B)= 1 4 , then P (A^ B^ ) is

Options

  1. A1 4
  2. B3 16
  3. C1 12
  4. D1 8

Correct answer

D. 1 8

Step-by-step solution

Given, P(A)= 1 2 , P(B)= 1 2 and P(A B)= 1 4 gathered P(A B)= P(A B) P(B) 1 4 = P(A B) 1 / 2 P(A B)= 1 4 1 2 = 1 8 gathered aligned & Now, P (A^ B^ )=P(A B)^ =1-P(A B) & =1-[P(A)+P(B)-P(A B)]=1- [ 1 2 + 1 2 - 1 8 ] & =1-1+ 1 8 = 1 8 aligned

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