Events A , B , C are mutually exclusive events such that P ( A )= 3 x +1 3 , P ( B )= x -1 4 and P ( C )= 1-2 x 4 . The set of possible values of x are in the interval.

Step-by-step solution

P ( A )= 3 x +1 3 , P ( B )= 1- x 4 , P ( C )= 1-2 x 2 These are mutually exclusive 0 3 x+1 3 1, 0 1-x 4 1 and 0 1-2 x 2 1-1 3 x 2,-3 x 1 and -1 2 x 1- 1 3 x 2 3 ,-3 x 1 , and - 1 2 x 1 2 Also 0 1+3 x 3 + 1-x 4 + 1-2 x 2 10 13-3 x 12 1 3 x 13 1 3 x 13 3 - 1 3 ,-3,- 1 2 , 1 3 x 2 3 , 1, 1 2 , 13 3 1 3 x 1 2 x [ 1 3 , 1 2 ]