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Question
A six sided die is marked ‘1’ on one face, ‘3’ on two of its faces, and ‘5’ on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find P(4 ≤ X < 10)
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Solution
Let X be the random variable denotes the total score in two thrown of a die.
Sample space S
| I\II | 1 | 3 | 3 | 5 | 5 | 5 |
| 1 | 2 | 4 | 4 | 6 | 6 | 6 |
| 3 | 4 | 6 | 6 | 8 | 8 | 8 |
| 3 | 4 | 6 | 6 | 8 | 8 | 8 |
| 5 | 6 | 8 | 8 | 10 | 10 | 10 |
| 5 | 6 | 8 | 8 | 10 | 10 | 10 |
| 5 | 6 | 8 | 8 | 10 | 10 | 10 |
n(S) = 36
X = {2, 4, 6, 8, 10}
| Values of the random variable | 2 | 4 | 6 | 8 | 10 | Total |
| Number of elements in inverse image | 1 | 4 | 10 | 12 | 9 | 36 |
Cumulative distribution function
P(4 ≤ X < 10) = P(X = 4) + P(X = 6) + P(X = 8)
= `4/36 + 10/36 + 12/36`
= `26/36`
= `13/18`
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