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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 |
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Solution
| 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(ωi) 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.
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