# Which of the following can not be valid assignment of probabilities for outcomes of sample space $S=\{\omega 1,\omega 2,\omega 3,\omega 4,\omega 5,\omega 6,\omega 7\}$

For an assignment to be considered valid,sum of all probabilities of each assignment should be 1
(a) Sum of all probabilities =0.1+0.01++0.05+0.03+0.01+0.2+0.6
$\Rightarrow 1$
$\therefore$ This is a valid assignment
(b) Sum of all the probabilities=$\large\frac{1}{7}+\frac{1}{7}+\frac{1}{7}+\frac{1}{7}+\frac{1}{7}+\frac{1}{7}+\frac{1}{7}$
$\Rightarrow \large\frac{7}{7}$
$\Rightarrow 1$
$\therefore$ This is a valid statement
(c) Sum of all the probabilities=0.1+0.2+0.3+0.4+0.5+0.6+0.7
$\Rightarrow 2.8$
$\therefore$ This is not a valid assignment because the sum of probabilities of each assignment is not 1
(d) This is not a valid assignment because the probability of any assignment cannot be negative.
Here probability of $\omega 1$ and $\omega 5$ are negative.
$\therefore$ Not a valid assignment
(e) This is not a valid assignment because the probability of $\omega 7=\large\frac{15}{14}$$> 1$
Hence the sum of all the probabilities > 1
$\therefore$ Not a valid assignment.