Rolling a Fair Die: Probability of Getting At Least One Six After Multiple Rolls

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Homework Help Overview

The discussion revolves around determining the number of rolls needed of a fair die to achieve a probability greater than 1/2 of rolling at least one six. The problem is situated within the context of probability theory.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants are considering the probability of rolling a six and exploring the complementary probability of not rolling a six across multiple rolls. There is an emphasis on calculating the threshold where the probability of at least one six exceeds 50%.

Discussion Status

Some participants have offered insights into calculating the probability of not rolling a six and suggest that this approach could lead to the desired outcome. There appears to be a shared understanding of the problem setup, but no consensus has been reached on the specific solution method.

Contextual Notes

Participants are working under the assumption that the die is fair and are focused on the probabilities associated with multiple rolls. The discussion includes repeated statements of the problem, indicating a need for clarification or deeper exploration of the concepts involved.

Amannequin
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Homework Statement
How many times do we need to roll a fair die to get a better than evens chance of at least one six?

The attempt at a solution
Let n be the number of rolls. Am I trying to find how large n must be so P(At least one six)≥ 1/2?
I'm working on the basis that I need to solve the probability of the union of events Ai, where Ai denotes the event of rolling i sixes, i =1,2,3..., being greater than 1/2.
Any help or nudge in the right direction will be appreciated.
 
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I'd attack it by finding the odds of NOT getting a six with one roll, then 2 rolls, then 3 rolls, and so on. As soon as that probability drops below 50% you've got the answer.
 
Amannequin said:
Homework Statement
How many times do we need to roll a fair die to get a better than evens chance of at least one six?

The attempt at a solution
Let n be the number of rolls. Am I trying to find how large n must be so P(At least one six)≥ 1/2?
I'm working on the basis that I need to solve the probability of the union of events Ai, where Ai denotes the event of rolling i sixes, i =1,2,3..., being greater than 1/2.
Any help or nudge in the right direction will be appreciated.

P(at least one six) = 1 - P(no sixes)
 
pasmith said:
P(at least one six) = 1 - P(no sixes)

Ah ... isn't that what I just said?
 

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