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प्रश्न
Three-digit numbers are formed using the digits 0, 2, 4, 6, 8. A number is chosen at random out of these numbers. What is the probability that this number has the same digits?
पर्याय
`1/16`
`16/25`
`1/645`
`1/25`
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उत्तर
`1/25`
Explanation:
Since a 3-digit number cannot start with digit 0.
The hundredth place can have any of the 4 digits.
Now, the tens and units place can have all the 5 digits.
Therefore, the total possible 3-digit numbers are 4 × 5 × 5
i.e., 100.
The total possible 3 digit numbers having all digits same = 4
Hence, P(3-digit number with same digits) = `4/100 = 1/25`.
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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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| (ii) |
\[\frac{1}{7}\]
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\[\frac{1}{7}\]
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\[\frac{1}{7}\]
|
\[\frac{1}{7}\]
|
\[\frac{1}{7}\]
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\[\frac{1}{7}\]
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\[\frac{1}{7}\]
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| (iv) |
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\[\frac{15}{14}\]
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