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AP EAMCET202124 Aug 2021Morning ShiftMathematicsProbabilityActual

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

Options

  1. A[ 1 3 , 1 2 ]
  2. B[ 1 3 , 2 3 ]
  3. C[ 1 3 , 13 3 ]
  4. D[0,1]

Correct answer

A. [ 1 3 , 1 2 ]

Step-by-step solution

A, B, C are mutually exclusive. aligned & P(A B C)=0, P(A B)=0, & P(B C)=P(C A)=0 & P(A)= 3 x+1 3 , P(B)= 1-x 4 , P(C)= 1-2 x 2 & P(A), P(B), P(C) [0,1] aligned Now, array lll 0 3 x+1 3 1 & 0 1-x 4 1 & 0 1-2 x 2 1 0 3 x+1 3 & 0 1-x 4 & 0 1-2 x 2 -1 3 x 2 & -1 -x 3 & -1 -2 x 1 - 1 3 x 2 3 & -3 x 1 & - 1 2 x 1 2 array aligned & P(A B C)=P(A)+P(B)+P(C)-P(A B) &-P(B C)-P(C A)+P(A B C) & P(A B C)=P(A)+P(B)+P(C) &= 3 x+1 3 + 1-x 4 + 1-2 x 2 &= 12 x+4+3-3 x+6-12 x 12 = 13-3 x 12 aligned aligned 0 & 13-3 x 12 1 0 & 13-3 x

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