What probability should be assigned to rolling a 4?

Question

For this problem, involving a weighted die, assume that the outcomes 1 through 4 are equally likely, that the outcomes 5 through 6 are equally likely, and that outcome 1 is 3 times as likely as outcome 5.

(1) What probability should be assigned to rolling a 4?


(2) What probability should be assigned to rolling a 6?

Answer 1

Nomenclature:

 

P1=probability of faces 1 to 4.

 

P6=probability of faces 5 to 6.

 

Probabilities must sum to 1.

 

4(P1)+2(P6)=1

 

Problem specifies:

 

(P1)=3(P5)=3(P6)

 

These are two equation in two unknowns.

 

4[3(P6)]+2(P6)=1

 

14(P6)=1

 

(P6)=1/14

 

(P1)=13/14

 

Probability of rolling a 4 is 13/14.

 

Probability of rolling a 6 is 1/14.