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

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The discussion revolves around calculating the probability of rolling at least a 5 on a die for 5 or more times out of 6 throws. It begins by establishing the basic probabilities of rolling a 5 or higher and less than 5 in a single throw. The conversation then shifts to analyzing the scenario where exactly 5 out of the 6 throws show a 5 or higher, requiring the identification of unique arrangements of the outcomes. The participants explore combinatorial arrangements to represent the outcomes visually. The thread emphasizes understanding both individual and combined probabilities in the context of multiple die throws.
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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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