Suppose a 6-sided die is weighted so that the probability of an outcome is proportional to the outcome.

That is, P(1)=x P(2)=2x P(3)=3x P(4)=4x P(5)=5x P(6)=6x (here x stands for a mystery number)

a) Find the value of x that would make this a valid probability model and then state the exact (in fraction form) probability of rolling each number on the die.

b) Which of the following events is more likely: rolling a 6 or rolling a or 1 2 ? Use work from part (a) to justify your answer.