Question

Which of the cannot be valid assignment of probability for elementary events or outcomes of sample space S =  {w₁, w₂, w₃, w₄, w₅, w₆, w₇}:

Elementary events:	w1	w2	w3	w4	w5	w6	w7
(ii)	\[\frac{1}{7}\]	\[\frac{1}{7}\]	\[\frac{1}{7}\]	\[\frac{1}{7}\]	\[\frac{1}{7}\]	\[\frac{1}{7}\]	\[\frac{1}{7}\]

Answer 1

w1	w2	w3	w4	w5	w6	w7
\[\frac{1}{7}\]	\[\frac{1}{7}\]	\[\frac{1}{7}\]	\[\frac{1}{7}\]	\[\frac{1}{7}\]	\[\frac{1}{7}\]	\[\frac{1}{7}\]

   Here, each of the numbers p(ω_i) is positive and less than 1.
    ∴ Sum of probabilities = \[p\left( \omega_1 \right) + p\left( \omega_2 \right) + p\left( \omega_3 \right) + p\left( \omega_4 \right) + p\left( \omega_5 \right) + p\left( \omega_6 \right) + p\left( \omega_7 \right)\]

= \[\frac{1}{7} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7} = 7 \times \frac{1}{7} = 1\]

  Thus, the assignment is valid.