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

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SUMMARY

The probability of rolling at least a 5 on a die for 5 or more times in 6 throws is calculated by considering the outcomes of each throw. Specifically, the event requires that 5 of the 6 throws show a 5 or 6, while one throw shows a number less than 5. The arrangement of these outcomes can be represented using combinatorial methods, where the unique arrangements of the throws are determined by the placement of the single throw less than 5 among the others.

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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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