What is the probability of getting 1,2,3,4 when 5 dice are thrown and

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Homework Help Overview

The discussion revolves around calculating the probability of rolling specific numbers (1, 2, 3, 4) when throwing five dice, with the condition that at least one die is not a 5. Participants express confusion regarding the interpretation of the problem and the conditions involved.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • One participant attempts to calculate the probability using a specific formula but is unsure about the correctness of their approach. Others question the clarity of the original question, seeking to understand whether the requirement is for at least one of each number or exactly one of each. There is also discussion about the implications of the fifth die's value.

Discussion Status

The discussion is ongoing, with participants clarifying the conditions of the problem and exploring different interpretations. Some guidance has been offered regarding the use of a multinomial distribution, but there is no consensus on the exact requirements of the problem.

Contextual Notes

Participants are grappling with the ambiguity of the problem statement, particularly regarding the conditions for the fifth die and the interpretation of the requirement for the numbers 1, 2, 3, and 4.

MilenaMath
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What is the probability of getting 1,2,3,4 when 5 dice are thrown and one of them is not 5.(the order of 1,2,3,4 doesn't matter)
I am really confused:
So I computed chances of getting correct numbers that is 1/6^4 times 5/6,then I multiply this by 4 times 5! Am I right?
 
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MilenaMath said:
What is the probability of getting 1,2,3,4 when 5 dice are thrown and one of them is not 5.(the order of 1,2,3,4 doesn't matter)
Your question is unclear. Do you mean at least one each of 1, 2, 3, 4? Exactly one of each?
When you say one of them is not five, do you mean that a particular one is not five, that they are not all five, or that none of them are five?
 


I need to get exactly 1,2,3,4(order doesn't matter) and the fifth dice can be whatever number but 5
 


Sorry, still not clear. If you get 4, 2, 2, 3, 1, is that ok or not?
 


MilenaMath said:
I need to get exactly 1,2,3,4(order doesn't matter) and the fifth dice can be whatever number but 5

From this description, it seems the event you want is
A = {1,1,2,3,4} or {1,2,2,3,4} or {1,2,3,3,4} or {1,2,3,4,4} or {1,2,3,4,6}, but without regard for order. Is that correct? If so, you can use a multinomial distribution to find
P{A} = p(2,1,1,1,0,0) + p(1,2,1,1,0,0) + ... + p(1,1,1,1,0,1), where these are the occupancy numbers in each of the 6 classes 1--6.

RGV
 

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