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प्रश्न
Seven persons are to be seated in a row. The probability that two particular persons sit next to each other is ______.
विकल्प
`1/3`
`1/6`
`2/7`
`1/2`
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उत्तर
Seven persons are to be seated in a row. The probability that two particular persons sit next to each other is `2/7`.
Explanation:
The two particular persons to be seated next each other then, they form one group.
Now the permutation of 6 persons = 6! × 2!
And Total number of permutations of 7 persons = 7!
∴ Required probability = `(6! xx 2!)/(7!)`
= `(6! xx 2)/(7 xx 6!)`
= `2/7`
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संबंधित प्रश्न
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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\[\frac{1}{7}\]
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