What is the value of w2?

Question

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

(1) What is the value of w2?

(2) What is the value of w1?

(3) What is the value of w3?

Answer 1

For 6 possibilities, and in terms of probability, let x represent 2, 4, 5, 6; let 3x represent the 1; and let 4(3x) = 12x represent the 3 :

 

So, x + x + x + x + 3x + 12x = 100%

 

4x + 3x + 12x = 100

 

19x = 100

 

x = 100/19

 

x = 5.263

 

 

A.) w2 is represented by an 'x'

 

w2 = 5.263% or 0.05263

 

 

B.) w1 is represented by '3x'

 

w1 = 3(5.263) = 15.789% or 0.15789

 

 

C.) w3 is represented by '12x'

 

w3 = 12(5.263) = YOUR CALCULATION, in terms of percent or decimal !