Chapter 6.2, Problem 23E

Which of the following probabilities are feasible for an experiment having sample space $\left\{s_1,s_2,s_3\right\}$ ? Explain your answer.

a. $\mathrm{Pr}\left(s_1\right)=.4,\mathrm{Pr}\left(s_2\right)=.4,\mathrm{Pr}\left(s_3\right)=.4$

b. $\mathrm{Pr}\left(s_1\right)=.5,\mathrm{Pr}\left(s_2\right)=.7,\mathrm{Pr}\left(s_3\right)=-.2$

c. $\mathrm{Pr}\left(s_1\right)=\frac{1}{5},\mathrm{Pr}\left(s_2\right)=\frac{2}{5},\mathrm{Pr}\left(s_3\right)=\frac{1}{5}$