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Question
Two numbers are selected from first six even natural numbers at random without replacement. If X denotes the greater of two numbers selected, find the probability distribution of X.
Solution
The two even natural numbers can be selected from the first six even natural numbers without replacement in 6 × 5 = 30 ways.
X represent the greater of two numbers.
Therefore, X can take the values 4, 6, 8, 10, 12.
For X = 4: Possible observations are (2, 4), (4, 2).
∴ P(X = 4) = `2/30 = 1/15`
For (X = 6): Possible observations are
(2, 6), (6, 2), (4, 6), (6, 4)
P(X = 6) = `4/30 = 2/15`
For X = 8: Possible observations are
(2, 8), (8, 2), (4, 8), (8, 4), (6, 8), (8, 6)
P(X = 8) = `6/30 = 1/5`
For X = 10: Possible observations are
(2, 10), (10, 2), (4, 10), (10, 4), (6, 10), (10, 6), (8, 10), (10, 8)
P(X = 10) = `8/30 = 4/15`
For X = 12: Possible observations are
(2, 12), (12, 2), (4, 12), (12, 4), (6, 12), (12, 6), (8, 12), (12, 8), (10, 12), (12, 10)
P(X = 12) = `10/30 = 1/3`
Therefore, the probability distribution
| X | 4 | 6 | 8 | 10 | 12 |
| P(X) | `1/15` | `2/15` | `1/5` | `4/15` | `1/3` |
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