6 Eli has four fair 4 -sided dice with sides labelled \(1,2,3,4\). He throws all four dice at the same time. The random variable \(X\) denotes the number of 2s obtained.
- Show that \(\mathrm { P } ( X = 3 ) = \frac { 3 } { 64 }\).
- Complete the following probability distribution table for \(X\).
| \(x\) | 0 | 1 | 2 | 3 | 4 |
| \(\mathrm { P } ( X = x )\) | \(\frac { 81 } { 256 }\) | | | \(\frac { 3 } { 64 }\) | \(\frac { 1 } { 256 }\) |
- Find \(\mathrm { E } ( X )\).
Eli throws the four dice at the same time on 96 occasions. - Use an approximation to find the probability that he obtains at least two 2 s on fewer than 20 of these occasions.