Step 1: Nonstandard dice can produce interesting distributions of outcomes. You

Question

Step 1:
Nonstandard dice can produce interesting distributions of outcomes. You have two balanced, six-sided dice. One is a standard die, with faces having 1, 2, 3, 4, 5, and 6 spots.
The other die has three faces with 0 spots and three faces with 6 spots. is the sum of the numbers on the up-faces when you roll these two dice.

What are the possible values of ?


1, 2, 3, 4, 5, 6 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 0, 1, 2, 3, 4, 5, 6 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12


Step 2:
Nonstandard dice can produce interesting distributions of outcomes. You have two balanced, six-sided dice. One is a standard die, with faces having 1, 2, 3, 4, 5, and 6 spots.
The other die has three faces with 0 spots and three faces with 6 spots. is the sum of the numbers on the up-faces when you roll these two dice.

Determine whether the following statement is True or False:
All outcomes are equally likely. True False

Explanation / Answer

Step-1

Y=sum of numbers on up fact

=Sum of {1,2,3,4,5,6] and {0,0,0,6,6,6}

={1,2,3,4,5,6,7,8,9,10,11,12}

Step-2

All outcomes are equally likely as shown below

P( a number in first die)=1/6

P(a number in second die)=3/6=1/2

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

Answer is TRUE

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