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प्रश्न
Six new employees, two of whom are married to each other, are to be assigned six desks that are lined up in a row. If the assignment of employees to desks is made randomly, what is the probability that the married couple will have nonadjacent desks?
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उत्तर
Number of desk occupied by one couple = 1
Only (4 + 1) = 5 persons to be assigned.
∴ Number of ways of assigning these 5 persons = 5! × 2!
Total number of ways of assigning 6 persons = 6!
∴ Probability that a couple has adjacent desk = `(5! xx 2!)/(6!) = 1/3`
So, the probability that the married couple will have no-adjacent desks = `1 - 1/3 = 2/3`.
Hence, the required probability = `2/3`.
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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 |
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| (ii) |
\[\frac{1}{7}\]
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\[\frac{1}{7}\]
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\[\frac{1}{7}\]
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\[\frac{1}{7}\]
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\[\frac{1}{7}\]
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\[\frac{1}{7}\]
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\[\frac{1}{7}\]
|
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