Which of the following cannot be a valid assignment of probabilities for outcomes of sample space $S = \{\omega_{1}, \omega_{2}, \omega_{3}, \omega_{4}, \omega_{5}, \omega_{6}, \omega_{7}\}$?
Outcome Probability $\omega_{1}$ $0.1$ $\omega_{2}$ $0.2$ $\omega_{3}$ $0.3$ $\omega_{4}$ $0.4$ $\omega_{5}$ $0.5$ $\omega_{6}$ $0.6$ $\omega_{7}$ $0.7$
| Outcome | Probability |
| $\omega_{1}$ | $0.1$ |
| $\omega_{2}$ | $0.2$ |
| $\omega_{3}$ | $0.3$ |
| $\omega_{4}$ | $0.4$ |
| $\omega_{5}$ | $0.5$ |
| $\omega_{6}$ | $0.6$ |
| $\omega_{7}$ | $0.7$ |
(A) For a probability assignment to be valid,it must satisfy two conditions:
$1$. Each probability $p(\omega_{i})$ must be such that $0 \leq p(\omega_{i}) \leq 1$.
$2$. The sum of all probabilities must be equal to $1$,i.e.,$\sum_{i=1}^{7} p(\omega_{i}) = 1$.
Let us calculate the sum of the given probabilities:
Sum $= 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 + 0.7 = 2.8$.
Since the sum $2.8 \neq 1$,this assignment of probabilities is not valid.
$1$. Each probability $p(\omega_{i})$ must be such that $0 \leq p(\omega_{i}) \leq 1$.
$2$. The sum of all probabilities must be equal to $1$,i.e.,$\sum_{i=1}^{7} p(\omega_{i}) = 1$.
Let us calculate the sum of the given probabilities:
Sum $= 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 + 0.7 = 2.8$.
Since the sum $2.8 \neq 1$,this assignment of probabilities is not valid.
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