what is the value of w3?

Question

for this problem, involving a weighted die, assume that 3, 6, 1, and 5 are equally likely, a 2 is three times as likely as a 5, and a 4 is four times as likely as a 2.

 

what is the value of w3?

what is the value of w2?

what is the value of w4?

Answer 1

Let w1 = w3 = w5 =w6 =  q   for some value q.   Then w2 = 3q and w4 = 12q.    Since the sum of the weights (actually probabilities of coming up) must be 1,  we conclude that  19 q = 1   or q = 1/19

 

Thus w3 =  1/19,   w2 = 3/19 and w4 = 12/19