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Question
Which of the following can not be valid assignment of probabilities for outcomes of sample space S = {ω1, ω2,ω3,ω4,ω5,ω6,ω7}
| Assignment | ω1 | ω2 | ω3 | ω4 | ω5 | ω6 | ω7 |
| (a) | 0.1 | 0.01 | 0.05 | 0.03 | 0.01 | 0.2 | 0.6 |
| (b) | `1/7` | `1/7` | `1/7` | `1/7` | `1/7` | `1/7` | `1/7` |
| (c) | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 |
| (d) | –0.1 | 0.2 | 0.3 | 0.4 | -0.2 | 0.1 | 0.3 |
| (e) | `1/14` | `2/14` | `3/14` | `4/14` | `5/14` | `6/14` | `15/14` |
Solution
(a) 0.1 + 0.01 + 0.05 + 0.03 + 0.01 + 0.2 + 0.6
= 1.00
The sum of the given probabilities of the events is 1.
So the given probability is valid.
(b) Sum of the given probabilities
= `1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7`
= `7/7`
= 1
∴ The given probability is valid.
(c) Sum of the given probabilities
= 0.1 + 0.1 + 0.3 + 0.4 + 0.5 + 0.6 + 0.7
= 2.7
This is more than one
So the given probability is not valid.
(d) The probability of any event cannot be negative.
Here two probabilities –0.1 and –0.2 are negative.
So the given probability is not valid.
(e) The sum of the given probabilities
`1/14 + 2/14 + 3/14 + 4/14 + 5/14 + 6/14+ 15/14`
= `36/14`
= `18/7`
which is more than one
So the given probability is not valid.
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