Elementary probability question: dice roll

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Homework Help Overview

The discussion revolves around a probability problem involving rolling a single die 12 times, where success is defined as rolling either a 4 or a 1. Participants are exploring the probability of achieving success or failure across these rolls.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning the clarity of the original problem statement and the definitions of success and failure. There is discussion about whether the probability should be considered on a per-roll basis or across all 12 rolls.

Discussion Status

The conversation is ongoing, with participants seeking clarification on the specific nature of the probability being asked. Some guidance has been offered regarding how to approach the calculation of failure probability, but no consensus has been reached on the interpretation of success and failure.

Contextual Notes

There is ambiguity in the problem regarding whether success is defined by achieving a 1 or 4 on any roll or if it requires a specific sequence of outcomes across all rolls. This uncertainty is affecting the direction of the discussion.

Mathman2013
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Homework Statement



Lets say you role a single honest dice 12 times. Where succes is either if the die shows 4 og 1 eye.

My question is what is the probability of sucess or failure?

Homework Equations

The Attempt at a Solution


Is it binomial or conditional probability?
 
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It is not clear to me what question you are asking. Please quote the problem exactly as given.
 
You roll one die 12 times if the die shows either 4 or a 1 it is success if it shows non 1 or non 4 for the remaining rolls then its a failture.

What is the probability of success or failure during the 12 rolls?
 
You are still not explaining what probability you are after very well. Are you after the probability of success/failure in one particular roll? If not, what do you consider success/failure during the 12 rolls?
 
So is it a success if we get a 1 or 4 on the first roll (not needing to roll anymore)? Is it also the same success if we fail 11 times and roll a 4 or 1 on the last roll?

If that is what you want, then you can do something like this: (prob of NOT rolling 1 or 4) AND (prob of NOT rolling 1 or 4) AND . . . AND (prob of NOT rolling 1 or 4).
Turn each of those AND's into multiplication, and assign a number for (prob of NOT rolling 1 or 4), and you have the probability that it will fail (Not rolling a 1 nor a 4 in 12 rolls).

Once you have that, calculating probability of success is straightforward.
 

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