4 A biased octagonal dice has faces numbered from 1 to 8 . The discrete random variable \(X\) is the score obtained when the dice is rolled once. The probability distribution of \(X\) is shown in the table below.
| \(x\) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| \(\mathrm { P } ( X = x )\) | \(p\) | \(p\) | \(p\) | \(p\) | \(p\) | \(p\) | \(p\) | \(3 p\) |
- Determine the value of \(p\).
- Find the probability that a score of at least 4 is obtained when the dice is rolled once.
The dice is rolled 30 times.
- Determine the probability that a score of 8 occurs exactly twice.