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
(iii)	0.7	0.06	0.05	0.04	0.03	0.2	0.1

Answer 1

w1	w2	w3	w4	w5	w6	w7
0.7	0.06	0.05	0.04	0.03	0.2	0.1

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

                                        = 0.7 +  0.6 + 0.5 + 0.4 + 0.3 + 0.2 + 0.1
                                         = 2.8 ≠ 1
       Thus, the assignment is not valid.