A biased four-sided die with faces labelled 1, 2, 3 and 4 is rolled and recorded. Let be the result…

A biased four-sided die with faces labelled 1, 2, 3 and 4 is rolled and recorded. Let $X$ be the result obtained when the die is rolled. The probability distribution for $X$ is given in the following table where $p$ and $q$ are constants.

$x$	1	2	3	4
$P(X=x)$	$p$	0·3	$q$	0·1

For the probability distribution, it is known that $E(X) = 2$. Find $p$ and $q$. Also, find $P(X > 2)$. Ajay plays a game with this four-sided die. In this game he is allowed a maximum of five rolls. His score is calculated by adding the results of each roll. He wins the game if his score is at least 10. After 3 rolls, Ajay has score of four points. Assuming that rolls of the die are independent, find the probability that Ajay wins the game.