Hello I have question on Element and Discrete Mathematics problem. I would like

Question

Hello I have question on Element and Discrete Mathematics problem. I would like to know step by step of solutions best/easiest way possible how to get the answer.( the answer to the table is already provided) The problem is : To compare two dice, consider making a chart with the columns labeled by the six numbers on one die( some of them duplicates) and the rows labeled by the six numbers of the other die ( some of them duplicates). Then put the corresponding numbers in each square and see in how many squares one die beats the other. If one die wins 24 of the 36 times, then that die will win two-thirds of the time. A chart for the die with three 5's and three 1's versus the die with four 4's and two blanks has been started for you. We want each square to look like a smaller copy of the entire rug.

Answer in the book provided this two tables

Each die beat the one next to it in the clockwise direction two-third of the time. 3 die ==> 6-2 die ==> 5-1 die==> 4-0 die==> 3 die==> 6-2 die==> same rotation.

1 1 1 5 5 5 0 (0,1)    (0,5) 0 (0,1) (0,5) 4 (4,1) (4,5) 4 (4,1) (4,5) 4 (4,1) (4,5) 4 (4,1) (4,5)

Explanation / Answer

Hi

i hope the question posted by you is a rolling around in Vegas die issue.

As per the problem there are 4 different type of die which are as follows:-

1) Two 6 ’ s and four 2 ’ s.

2) Three 5 ’ s and three 1 ’ s.

3) Four 4 ’ s and two blank faces.

4)The last die has 3 ’ s on each face

No die can win the game with all other die there will be always one die which will win from the die choosen and the aurthor has given a clockwise sequence which is stated in the question as well.

The solution is that winning dice has to win 2/3 times from the other times and it is only possible if a dice has number higher than the other dice 2/3 or 4 times.

In simple language a dice will win if it has 4 faces having higher numbers as compared to the other dice.

So as per the data in question die with four 4 ’ s and two blanks beats the die with all 3 ’ s two - thirds of the time because it has four faces wih higher number as compared to the ther dice.

One more thing if both the die are normal die i.e. each of them have 1,2,3,4,5,6 on them then the probabilit of both the winning will be 1/2 for both of them.

Hope it answer your question.

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