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If the events A and B are mutually exclusive events such that P ( A )= 3 x+1 3 and P ( B )= 1-x 4 , then the set of possible values of x lies in the interval :

Options

  1. A[0,1]
  2. B[ 1 3 , 2 3 ]
  3. C[- 1 3 , 5 9 ]
  4. D[- 7 9 , 4 9 ]

Correct answer

C. [- 1 3 , 5 9 ]

Step-by-step solution

Since events A and B are mutually exclusive aligned & P ( A )+ P ( B )=1 & 3 x+1 3 + 1-x 4 =1 & 12 x+4+3-3 x=12 & 9 x=5 x= 5 9 & x [- 1 3 , 5 9 ] aligned

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