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Question
A and B throw a pair of dice. If A throws 9, find B's chance of throwing a higher number.
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Solution
A and B throw a pair of dices.
Then all the possible outcomes = 62 = 36
i.e. total number of possible outcome, n(S) = 36
Consider E = event where A throws 9 and B throws more than 9, i.e. 10, 11 and 12
E = {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}
i.e. n(E) = 6
Hence, required probability = \[\frac{6}{36} = \frac{1}{6}\]
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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` |
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