Nonstandard dice can produce interesting distributions of outcomes. You have two

Question

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.

What are the possible values for the total number of spots Y on the up-faces when you roll these two dice? (Enter your answers as a comma-separated list.) Each value will have the same probability.

What is this probability? (Enter your answer as a fraction.)

Explanation / Answer

ans=

Here is a table of the possible observations ofYthat can occur when we roll one standard dieand one “weird” die.There are 36 possible pairs of faces; however, a number of the pairs areidentical to each other

die1 die 2 .. 0 .... 0 .... 0 .... 6 .... 6 .... 6
... 1 ............ 1 .... 1 .... 1 .... 7 .... 7 .... 7
... 2 ............ 2 .... 2 .... 2 .... 8 .... 8 .... 8
... 3 ............ 3 .... 3 .... 3 .... 9 .... 9 .... 9
... 4 ............ 4 .... 4 .... 4 ... 10 ... 10 ... 10
... 5 ............ 5 .... 5 .... 5 ... 11 ... 11 ... 11
... 6 ............ 6 .... 6 .... 6 ... 12 ... 12 ... 12


thus each value from 1 to 12 will have a value of 3/36 = 1/12
Y is a discrete uniform distribution from 1 to 12

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.