Two dice are rolled. Let X be the maximum number obtained. (Thus, if 1 and 2 are rolled, X = 2; if 5 and 5 are rolled, X = 5.) Assume that all 36 elements of the sample space are equally likely. Find the probability function for X. That is, find P(X = x), for x = 1, 2, 3, 4, 5, 6.
| x | P(X=x) |
| 1 | 1//36 |
| 2 | 3//36 |
| 3 | 5//36 |
| 4 | 7//36 |
| 5 | 9//36 |
| 6 | 11//36 |
following number pair on dice 1 and dice 2 are shown and corresponding X is denoted according to question. each number pair has probability 1/36
| number pair | X | number pair | X | number pair | X |
| (1,1) | 1 | (1,2) | 2 | (1,3) | 3 |
| (2,1) | 2 | (2,2) | 2 | (2,3) | 3 |
| (3,1) | 3 | (3,2) | 3 | (3,3) | 3 |
| (4,1) | 4 | (4,2) | 4 | (4,3) | 4 |
| (5,1) | 5 | (5,2) | 5 | (5,3) | 5 |
| (6,1) | 6 | (6,2) | 6 | (6,3) | 6 |
| number pair | X | number pair | X | number pair | X |
| (1,4) | 4 | (1,5) | 5 | (1,6) | 6 |
| (2,4) | 4 | (2,5) | 5 | (2,6) | 6 |
| (3,4) | 4 | (3,5) | 5 | (3,6) | 6 |
| (4,4) | 4 | (4,5) | 5 | (4,6) | 6 |
| (5,4) | 5 | (5,5) | 5 | (5,6) | 6 |
| (6,4) | 6 | (6,5) | 6 | (6,6) | 6 |
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