Question

$\sum_{i=1}^{n}p(x_{i} )$ is equal to

(a) 0
(b) 1
(c) -1
(d) ∞

Answer 1

It is fact that probability of any natural phenomena can't be greater than 1 and can't less than zero.
e.g., 0 ≤ P(x) ≤ 1

Here ,P(S) = $\bold{\sum_{i=1}^n{P(x_i)}}$
Means,P(S) = $\bold{\sum_{i=1}^n{P(x_i)}}$ = P(x₁) + P(x₂) + P(x₃) + ........ + P(xₙ)
of course P(S) is the sum of probabilities , but As you know, P(S) is also a probability . Hence, it maximum can be 1 .
P(S) ≠ 0 because , in the sum of All terms no one is negative .

Hence, we have best choice P(S) = 1
e.g., $\bold{\sum_{i=1}^n{P(x_i)}}$ = 1

Hence , option (b) is correct