Math CentralQuandaries & Queries


Question from dilys, a student:

Two fair dice are thrown. Find the probability that the difference of the two numbers is divisible by 4?

We have two responses for you

There are only 36 possible outcomes when two dice are thrown. Why not list all 36 outcomes and circle those where the difference of the two numbers is divisible by 4? After finding the correct answer, you should then look carefully at what you have done and figure out a much faster way to get that answer.



If the dice are fair then every possibility is equally likely. Start this problem by writing down two columns of numbers, one for die 1 (D1) and one for die 2 (D2)

D1 D2
1 1
1 2
1 3
1 4
1 5
1 6
2 1
2 2
. .
. .
. .
6 6

This list should represent all possible rolls of two fair six-sided dice. How many entries are in the list? -- call this number 'n'. Next put a check mark beside each entry where the difference is divisible by four. How many checkmarks did you use? -- call this number 'x'. Then you will know that 'x' out of 'n' rolls have a difference divisible by 4. Express this as a fraction and you will have the probability.

L. Dame

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