7 A fair die has one face numbered 1, one face numbered 3, two faces numbered 5 and two faces numbered 6 .
- Find the probability of obtaining at least 7 odd numbers in 8 throws of the die.
The die is thrown twice. Let \(X\) be the sum of the two scores. The following table shows the possible values of \(X\).
\begin{table}[h]
\captionsetup{labelformat=empty}
\caption{Second throw}
| | 1 | 3 | 5 | 5 | 6 | 6 |
| \cline { 2 - 8 } | 1 | 2 | 4 | 6 | 6 | 7 | 7 |
| 3 | 4 | 6 | 8 | 8 | 9 | 9 |
| First | 5 | 6 | 8 | 10 | 10 | 11 | 11 |
| throw | 5 | 6 | 8 | 10 | 10 | 11 | 11 |
| 6 | 7 | 9 | 11 | 11 | 12 | 12 |
| 6 | 7 | 9 | 11 | 11 | 12 | 12 |
- Draw up a table showing the probability distribution of \(X\).
- Calculate \(\mathrm { E } ( X )\).
- Find the probability that \(X\) is greater than \(\mathrm { E } ( X )\).