question_answer

If the sample space of an experiment is\[S=({{\omega }_{1}},{{\omega }_{2}},{{\omega }_{3}})\], then which of the following assignment of probabilities is valid?

A)  \[P({{\omega }_{1}})=\frac{1}{2},P({{\omega }_{2}})=\frac{1}{3},P({{\omega }_{3}})=\frac{2}{3}\]

B)  \[P({{\omega }_{1}})=\frac{1}{2},P({{\omega }_{2}})=\frac{1}{3},P({{\omega }_{3}})=\frac{1}{4}\]

C)  \[P({{\omega }_{1}})=\frac{1}{2},P({{\omega }_{2}})=\frac{1}{3},P({{\omega }_{3}})=\frac{-1}{6}\]

D)  \[P({{\omega }_{1}})=\frac{1}{2},P({{\omega }_{2}})=\frac{1}{3},P({{\omega }_{3}})=\frac{1}{6}\]