Probability of Sum in 3-Side Die: Answers Needed!

In summary, the conversation discusses the possibility of finding general formulas to answer questions about the probability of getting specific sums when throwing a 3-side die 100 times. While there are formulas available, they may not be as simple as expected.
  • #1
encapuchado
3
0
Hi,

I've looking in the internet but I can't find a straight answer.

The problem is this:

Suppose we have a 3-side die (faces marked 0, 1, and 2).

Are there general formulas to answer questions such as:

a) "After throwing the die 100 times, get the probability of the sum being 120"?
b) "After throwing the die 100 times, get the probability of the sum being greater or equal to 120"?

Any help is appreciated.


P.S. This is not homework, I'm too old to be a student ;-)
 
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  • #3
I saw the message and he/she doesn't have a complete answer.
 
  • #4
Neither do I. What I can tell you is, "yes, there are such general formulas."
 
  • #5
Last edited:

1. What is the probability of rolling a sum of 7 on a 3-sided die?

The probability of rolling a sum of 7 on a 3-sided die is 1/3, or approximately 33.33%. This is because there are 3 possible outcomes for each roll (1, 2, or 3), and only one of those outcomes (3) will result in a sum of 7 when added to the other two rolls.

2. How does the probability change if we roll two 3-sided dice?

If we roll two 3-sided dice, the probability of getting a sum of 7 increases to 2/9, or approximately 22.22%. This is because there are now 9 possible outcomes (3*3), and only two of those outcomes (1+6 and 2+5) will result in a sum of 7.

3. Is the probability of rolling a sum of 7 the same for each roll?

Yes, the probability of rolling a sum of 7 is the same for each roll. This is because each roll is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability remains constant for each roll.

4. What is the probability of rolling a sum of 3 on a 3-sided die?

The probability of rolling a sum of 3 on a 3-sided die is also 1/3, or approximately 33.33%. This is because there is only one possible outcome (1+1+1) that will result in a sum of 3.

5. How does the probability change if we roll three 3-sided dice?

If we roll three 3-sided dice, the probability of getting a sum of 3 increases to 1/27, or approximately 3.70%. This is because there are now 27 possible outcomes (3*3*3), and only one of those outcomes (1+1+1) will result in a sum of 3.

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