What is the probability that at least 5 was shown for 5 or more times?

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Discussion Overview

The discussion revolves around calculating the probability of rolling a die six times and determining the likelihood that the outcome of at least 5 appears five or more times. The scope includes probability theory and combinatorial arrangements related to dice rolls.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant poses the initial question regarding the probability of rolling at least a 5 for five or more times in six throws.
  • Another participant seeks clarification on the interpretation of the event described in the initial question.
  • Participants discuss the probabilities associated with a single die throw, noting that the probability of rolling at least a 5 is 2/6, while the probability of rolling less than 5 is 4/6.
  • Further exploration is suggested regarding the scenario where exactly five out of six throws result in at least a 5, prompting a combinatorial analysis of arrangements of the outcomes.

Areas of Agreement / Disagreement

The discussion includes multiple viewpoints and interpretations of the initial question, with no consensus reached on the probability calculation or the arrangement analysis.

Contextual Notes

Participants have not yet resolved the mathematical steps needed to calculate the probability for the scenario of interest, and assumptions regarding the arrangement of outcomes remain unaddressed.

Hasib
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A dice was thrown for 6 times.What is the probability that at least 5 was shown for 5 or more times?
 
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Hi Hasib, welcome to MHB.

What do you make of the event that says at least 5 was shown for 5 or more times?
 
Suppose we throw a die one time, what is the probability that at least a 5 is shown? What is the probability that less than 5 is shown?
 
MarkFL said:
Suppose we throw a die one time, what is the probability that at least a 5 is shown? What is the probability that less than 5 is shown?
2/6 and 4/6 = 1/3 and 2/3
 
Hasib said:
2/6 and 4/6 = 1/3 and 2/3

Okay good, Now we have to consider 6 throws. Let's examine the case where 5 of the 6 throws is at least 5 (5 or 6). That means one throw is less than 5. Suppose we represent this one throw less than 5 with a red cube and the others with identical green cubes and line them up in a row. How many unique arrangements would we have?
 

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