Question

two fair dice, each with at least 6 faces are rolled. on each face of each dice is printed a distinct integer from 1 to the number of faces on that die, inclusive. the probability of rolling a sum of 7 is 3 4 of the probability of rolling a sum of 10, and the probability of rolling a sum of 12 is 1 12 . what is the least possible number of faces on the two dice combined?

Answer 1

Using the Counting the faces of two dice,

the atleast 17 number of faces are possible on the combination of two dice.

First, we have to count the favorable cases,

We know both dice have atleast 6 faces.

It gives 6 favorable cases for a sum of 7.

If we can count them if mean even if dice had more than 6 faces, will matter of for sum of 7.

Now, the mean, we need 6× 4/3=8 (favorable cases for the sum of 10)

If we count 3 favorable cases for each having 6 faces.

For more than 9 faces on a dice matter give the denominator (sample space) are the same for both sum of 7 and the sum of 10, and the probability of one is in proportion to the other.

It mean, additional 5 cases must be ( 7,2), (2,7), (8,2), (2,8) ,(9,1)

So , one of the dice has 8 faces and the other has atleast 9 faces.

Now, we must have atleast 17 combined faces of two dice for probability . So, we get if 12 with configration of 8 faces on one dice.

To learn more about Counting faces of combined dice, refer:

https://brainly.com/question/1302068

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