Question

Nonstandard dice can produce interesting distributions of outcomes. You have two balanced, six-sided dice. One is a standard die, with faces having one, two, three, four, five, and six spots. the other die has three faces with one spot and three faces with six spots. find the probability distribution for the total number of spots Y on the up-faces when you roll these two dice

Answer 1

et outcome (a,b) is first die shows an a and other shows a b

below is e probability distribution for the total number of spots Y

P(Y=2) =P(1,1) =(1/6)*(1/2)=1/12

P(Y=3)=P(2,1) =(1/6)*(1/2)=1/12

P(Y=4)=(1/12)

P(Y=5)=1/12

P(Y=6)=1/12

P(Y=7)=P(1,6)+P(6,1) =(1/6)*(1/2)+(1/6)*(1/2) =1/6

P(Y=8)=P(2,6)=1/12

P(Y=9)=1/12

P(Y=10)=1/12

P(Y=11)=1/12

P(Y=12)=1/12