1 The score when two fair six-sided dice are thrown is the sum of the two numbers on the upper faces.
- Show that the probability that the score is 4 is \(\frac { 1 } { 12 }\).
The two dice are thrown repeatedly until a score of 4 is obtained. The number of throws taken is denoted by the random variable \(X\). - Find the mean of \(X\).
- Find the probability that a score of 4 is first obtained on the 6th throw.
- Find \(\mathrm { P } ( X < 8 )\).