What is the value of w3? What is the value of w4? What is the value of w1?

Question

For this problem, assume that 3, 6, 5, and 2 are equally likely, a 4 is four times as likely as a 2, and a 1 is twice as likely as a 4.

Answer 1

The sum of all the probabilities must be 1  

 

Let P(3) = X

Then P(6) = P(5) = P(2) = X

P(4) = 4X

P(1) = 2P(4) = 2(4X) = 8X

 

So X + X + X + X + 4X + 8X = 1

16X = 1

X = 1/16

 

I don't know what w3, w4 and w1 represent, but 

 

P(3) = X = 1/16

P(4) = 4X = 4/16 = 1/4

P(1) = 8X = 8/16 = 1/2