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

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In summary, the conversation discusses the probability of rolling at least a 5 on a die and the probability of rolling less than a 5. The conclusion is that for 6 throws, there is a 1/3 chance of getting at least 5 for 5 or more times and a 2/3 chance of getting less than 5. Additionally, for the specific case of 5 out of 6 throws being at least 5, there are multiple unique arrangements that can occur.
  • #1
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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  • #2
Hi Hasib, welcome to MHB.

What do you make of the event that says at least 5 was shown for 5 or more times?
 
  • #3
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?
 
  • #4
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
 
  • #5
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?
 

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

What does "probability" mean in this context?

In this context, probability refers to the likelihood or chance of a specific outcome occurring. It is often expressed as a decimal, fraction, or percentage.

How is the probability of at least 5 being shown calculated?

The probability of at least 5 being shown is calculated by dividing the number of desired outcomes (in this case, 5 or more) by the total number of possible outcomes. This is known as the probability formula: P(A) = desired outcomes / total outcomes.

What is the difference between "at least" and "exactly" in this question?

"At least" means that the desired outcome can occur equal to or more than the specified number of times. In this case, it could be 5, 6, 7, and so on. "Exactly" means that the desired outcome must occur exactly the number of times specified, in this case, 5 times.

How does the number of trials affect the probability of at least 5 being shown?

The number of trials has a direct impact on the probability of at least 5 being shown. As the number of trials increases, the probability of at least 5 being shown also increases. This is because with more trials, there are more opportunities for the desired outcome to occur.

Can the probability of at least 5 being shown ever be 100%?

No, the probability of at least 5 being shown can never be 100%. This is because there is always a possibility of other outcomes occurring, even if it is a very small chance. However, as the number of trials increases, the probability can approach 100% but will never reach it.

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