A 6-sided die is weighted so that 1,2, and 3 show up equally likely, 4, 5, 6 show up equally likely, and 4 shows up twice as often as 1.

Find the probability distribution for when this die is rolled.a.

What is the probability that, when this die is rolled, that an even number shows up? What is the probability that a prime number (2, 3, 5) shows up?b.

My Answers:

1, 2, 3, 5, and 6 have the probability of 1/6 ... and 4 = 1/3a.

Probability an even number is rolled = 1/2 ... Odd number = 2/3b.

I'm taking a complete shot in the dark at this so any help would be appreciated. Is there any specific formula I should be using?