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Let A and B be two events such that P( A B )= 1 6 , P(A B)= 1 4 and P( A )= 1 4 , where A stands for complement of event A . Then events A and B are

Options

  1. Aequally likely and mutually exclusive
  2. Bequally likely but not independent
  3. Cindependent but not equally likely
  4. Dmutually exclusive and independent

Correct answer

C. independent but not equally likely

Step-by-step solution

aligned & P( A B )= 1 6 , P(A B)= 1 4 and P( A )= 1 4 & P(A B)=5 / 6 P(A)=3 / 4 & Also P(A B)=P(A)+P(B)-P(A B) & P(B)=5 / 6-3 / 4+1 / 4=1 / 3 & P(A) P(B)=3 / 4-1 / 3=1 / 4=P(A B) aligned Hence A and B are independent but not equally likely.

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