Three fair six sided dice are rolled. What is the probability that the sum of the outcome is 6? *Round your answer to the third decimal place.

Question

Finite Math.. If you could also explain how you got the answer that would be awesome!

Answer 1

I won't give you the answer yet, but let me push you in the right direction.

 

You should begin by trying to answer this question:

Q1) "When I roll the 3 dice, how many options are there?"

 

When you go about answering this question, you could enumerate all of the possibilities:

1, 1, 1

1, 1, 2

1, 1, 3

.....

2, 1, 1

2, 1, 2

....

 

But you'll find that that is very time consuming. Try to think of a way to determine how many possibilities there are without writing every single one down. Look for patterns, and extrapolate.

 

Once you know how many options there are (let's say there's N options), it's should be relatively trivial to understand that any single time you roll the 3 dice, you have a one-in-N chance.

 

For example, when you roll only one die, there are 6 possible outcomes. So for any of the given faces / values you have a 1-in-6 chance of getting each distinct value.

 

Suppose you find that the answer is 100 for (Q1) above. Now you know that any time you roll the 3 dice, any ONE of those possibilities has a 1-in-100 chance of occurring.

NOTE: 100 is not the correct answer for Q1, this is simply for the sake of example.

 

 

After you've determined all of that, the next question you want to answer is:

Q2) "How many of those options sum up to 6?"

Again, you could time consumingly sum all of the possibilities to find which sum to six, like this:

1, 1, 4

1, 4, 1

2, 3, 1

... etc.

 

But again, the point of problems like this is to NOT have to write out every possibility. Imagine if you were asked the same problem, but there were 100 dice, and you were asked what the chances were that the faces on the dice added up to 239? This would take you a long time to write out all of the possibilities and sum them all up.

 

Again, write out a few perhaps and see if you can find any pattern and work from there.

 

You might also simplify the problem, i.e. "Roll only 2 dice, and find the probability that the sum of the faces sum to 7" doing this one manually shouldn't be difficult, and after you've done it, maybe you'll gain some insight on how to come up with a generic way to solve the more complex problems.

Answer 2

Hello Brittany.

 

For any probability problem, you need the total number of possible outcomes as your denominator. In this case that number is 6³ = 316 since each die has six sides.

 

For our denominator, how many ways are there of getting a sum of 6?

 

Systematically list the possibilities. I'll list all the ways of the first die being one, then of it being two, then of it being 3. By the time I get to the end, all possible combinations will have been listed:

 

1st die          2nd die          3rd die

1                       1                     4

1                       2                     3

1                       3                     2

1                       4                     1

2                       1                     3

2                       2                     2

2                       3                     1

3                       1                     2

3                       2                     1

4                       1                     1

Scratch your head as much as you want, but there are only these 10 ways of throwing 3 dice to get a sum of 6. Your probability of a sum equal to exactly 6, then, is 10/316 = 0.032 (rounded to third decimal place).