4 A certain four-sided die is biased. The score, \(X\), on each throw is a random variable with probability distribution as shown in the table. Throws of the die are independent.
| \(x\) | 0 | 1 | 2 | 3 |
| \(\mathrm { P } ( X = x )\) | \(\frac { 1 } { 2 }\) | \(\frac { 1 } { 4 }\) | \(\frac { 1 } { 8 }\) | \(\frac { 1 } { 8 }\) |
- Calculate \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).
The die is thrown 10 times.
- Find the probability that there are not more than 4 throws on which the score is 1 .
- Find the probability that there are exactly 4 throws on which the score is 2 .