If the events A and B are mutually exclusive events such that P(A) = `(3x + 1)/(3)` and P(B) = `(1 - x)/(4)`, then the set of possible real values of x lies in the intervalA. [0, 1]B. `[-(1)/(3), (5)/(9)]`C. `[-(7)/(9),(4)/(9)]`D. `[(1)/(3),(2)/(3)]`

If the events A and B are mutually exclusive events such that P(A) = `

1.	If the events A and B are mutually exclusive events such that P(A) = `(3x + 1)/(3)` and P(B) = `(1 - x)/(4)`, then the set of possible real values of x lies in the intervalA. [0, 1]B. `[-(1)/(3), (5)/(9)]`C. `[-(7)/(9),(4)/(9)]`D. `[(1)/(3),(2)/(3)]`
Answer» Correct Answer - B We must have, `0 le P(A) le 1` implies `0 le (3x + 1)/(3) le 1` implies `(-1)/(3) le x le (2)/(3)" (1)"` and `0le P(B) le 1` implies `0 le (1-x)/(4) le 1` implies `-3 le x le 1 " (2)"` and `0le P(A uu B) = P(A) + P(B) le 1` `implies 0 le (3x + 1)/(3) + (1 - x)/(4) le 1` implies `(-7)/(9) le x le (5)/(9) " (3)"` From (1), (2) and (3), we get x `in [(-1)/(3), (5)/(9)]`.

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If the events A and B are mutually exclusive events such that P(A) = `(3x + 1)/(3)` and P(B) = `(1 - x)/(4)`, then the set of possible real values of x lies in the intervalA. [0, 1]B. `[-(1)/(3), (5)/(9)]`C. `[-(7)/(9),(4)/(9)]`D. `[(1)/(3),(2)/(3)]`

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