Events A, B, C are mutually exclusive events such that `P(A)=(3x+1)/(3), P(B)=(1-x)/(4) " and " P(C )=(1-2x)/(2)`. The set of all possible values of x are in the intervalA. [0, 1]B. `[-1//3, 1//2]`C. `[1//3, 2//3]`D. `[1//3, 13//3]`

Events A, B, C are mutually exclusive events such that `P(A)=(3x+1)/(3

1.	Events A, B, C are mutually exclusive events such that `P(A)=(3x+1)/(3), P(B)=(1-x)/(4) " and " P(C )=(1-2x)/(2)`. The set of all possible values of x are in the intervalA. [0, 1]B. `[-1//3, 1//2]`C. `[1//3, 2//3]`D. `[1//3, 13//3]`
Answer» Correct Answer - B It is given that the events A, B, C, are mutually exclusive. Therefore, `P(A) ge 0, P(B) ge 0, P(C ) ge 0, " and " P(A cup B cup C) ge 0` `implies P(A) ge 0, P(B) ge 0, P(C ) ge 0, " and "P(A)+P(B)+P(C ) ge0` `implies (3x+1)/(3) ge 0, (1-x)/(4) gt 0, (1-2x)/(2) ge 0`, and, `(3x+1)/(3)+(1-x)/(4)+(1-2x)/(2) ge 0` `implies x gt -(1)/(3), x le 1, x le (1)/(2) " and" 1-3x gt 0` `implies -(1)/(3) le x le (1)/(2) " and " x le (1)/(3)` `implies -(1)/(3) le x le (1)/(2) implies x in [-1//3, 1//2]`

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Events A, B, C are mutually exclusive events such that `P(A)=(3x+1)/(3), P(B)=(1-x)/(4) " and " P(C )=(1-2x)/(2)`. The set of all possible values of x are in the intervalA. [0, 1]B. `[-1//3, 1//2]`C. `[1//3, 2//3]`D. `[1//3, 13//3]`

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