SOLUTION: If two tetrahedral dice is thrown , find the probability that 1. the sum of the two scores is 5 2. the difference of the two scores is 1 3. the product of the two scores is 4

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Question 1193761: If two tetrahedral dice is thrown , find the probability that
1. the sum of the two scores is 5
2. the difference of the two scores is 1
3. the product of the two scores is 4
Found 2 solutions by math_tutor2020, Edwin McCravy:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Problem 1

I'm assuming the four sides of the tetrahedral dice are labeled 1,2,3,4
There are two ways to sum to 5 and they are:
1+4 = 5
4+1 = 5

This is out of 4*4 = 16 ways to throw the two four-sided dice.

So 2/16 = 1/8 is the probability we want.

Answer: 1/8

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Problem 2

Here are the ways to get a difference of 1, where the first die is larger than the second and I'm subtracting in the format first-second
4-3 = 1
3-2 = 1
2-1 = 1

Now let's assume that the second die is the larger of the pair and we subtract using absolute value so we get a positive result
|3-4| = 1
|2-3| = 1
|1-2| = 1
again I'm subtracting in the format first-second, but the absolute value bars ensure the result is never negative.

We have 6 such ways to get the two dice to be separated by 1. This is out of the 4*4 = 16 ways to throw the two dice.

6/16 = 3/8

Answer: 3/8


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Problem 3

Here are all of the ways the two dice could multiply to 4
1*4 = 4
2*2 = 4
4*1 = 4
There are 3 ways to get what we want out of 16 ways to throw the dice.

Answer: 3/16
Answer by Edwin McCravy(20063)   (Show Source): You can put this solution on YOUR website!

Oh crap! the other tutor did it for you.
Too bad!

Here are all possible ways the tetrahedral dice can be thrown.

(1,1) (1,2) (1,3) (1,4)
 
(2,1) (2,2) (2,3) (2,4) 
 
(3,1) (3,2) (3,3) (3,4) 
 
(4,1) (4,2) (4,3) (4,4)

How many is that?

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Here are all the ways the tetrahedral dice can fall.
The ones with sum 5 are in red:

(1,1) (1,2) (1,3) (1,4) 
 
(2,1) (2,2) (2,3) (2,4) 
 
(3,1) (3,2) (3,3) (3,4)  
 
(4,1) (4,2) (4,3) (4,4) 

That's how many out of how many? Make a fraction, and reduce it. 

--------------------------------------------------------------

Here are all the ways the tetrahedral dice can fall.
The ones with a difference of 2 are in red:

(1,1) (1,2) (1,3) (1,4)
 
(2,1) (2,2) (2,3) (2,4) 
 
(3,1) (3,2) (3,3) (3,4) 
 
(4,1) (4,2) (4,3) (4,4) 

That's how many out of how many? Make a fraction and reduce it

-------------------------------------------------------

Here are all the ways the tetrahedral dice can fall.
The ones with product 4 are in red:

(1,1) (1,2) (1,3) (1,4)
 
(2,1) (2,2) (2,3) (2,4) 
 
(3,1) (3,2) (3,3) (3,4) 
 
(4,1) (4,2) (4,3) (4,4)

That's how many out of how many? Make a fraction, and reduce it if possible.

Edwin
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