MHB What is the Probability of Rolling a Number 6 Four Times in a Row on a Dice?

AI Thread Summary
The discussion revolves around calculating the probability of rolling a six four times in a row on a die, given that a six appeared 14 times in 100 rolls. The method proposed involves determining the total arrangements of rolling a six 14 times and then finding the arrangements where six is rolled four consecutive times. The probability formula provided is based on the binomial distribution, assuming a fair die with a probability of one-sixth for rolling a six. However, some participants raise concerns about the clarity of the question, questioning whether it pertains to a single run of four sixes or multiple runs. Overall, the conversation emphasizes the need for precise definitions in probability calculations.
Essential06
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Can anyone help me with this one please...

If i roll a dice 100 times and number 6 comes out on 14 occassions (14%) what would have been the probability of number 6 being rolled 4 times in a row? (as a percentage?)

If someone would be so kind to tell me how to calculate this in simple terms i'd be really grateful. Thanks
 
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Re: Probability Help Please

Essential06 said:
Can anyone help me with this one please...

If i roll a dice 100 times and number 6 comes out on 14 occasions (14%) what would have been the probability of number 6 being rolled 4 times in a row? (as a percentage?)

If someone would be so kind to tell me how to calculate this in simple terms i'd be really grateful. Thanks

Hi Essential06, :)

Let me summarize the method that I will use to solve this problem.

Find the number of arrangements with 6 rolling out on 14 occasions(we shall take this as \(x\)). Then among those outcomes with 14 sixes find the number of arrangements where 6 is rolled 4 times in a row(we shall take this as \(y\)). Supposing that each outcome with 6 being rolled 4 times in a row is equally likely to happen,

The probability of getting 6 rolled 4 times in a row is, \(\dfrac{y}{x}\).

Hope you can continue.

Kind Regards,
Sudharaka.
 
Re: Probability Help Please

Essential06 said:
Can anyone help me with this one please...

If i roll a dice 100 times and number 6 comes out on 14 occassions (14%) what would have been the probability of number 6 being rolled 4 times in a row? (as a percentage?)

If someone would be so kind to tell me how to calculate this in simple terms i'd be really grateful. Thanks

If p is the probability of the number six in each roll, then the probability to have 4 six in 10 rolls is,,,

$\displaystyle P= \binom {10}{4} p^{4}\ (1-p)^{6}$ (1)

If the dice is 'non loaded' then is $\displaystyle p=\frac{1}{6} = .16666666666...$ and that is compatible with 14 six in 100 rolls. If $\displaystyle p=\frac{1}{6}$ then the (1) gives $\displaystyle P= .05426587585...$...

Kind regards

$\chi$ $\sigma$
 
Re: Probability Help Please

Essential06 said:
If i roll a dice 100 times and number 6 comes out on 14 occassions (14%) what would have been the probability of number 6 being rolled 4 times in a row? (as a percentage?)
I for one would like you to explain exactly what this question means.
Are you asking about exactly one run of four 6's?
Or could there be three runs of four 6's.? If so do they have to be separated?
If not how do you count a run of six 6's?
This question is so ill-defined as to be unanswerable.
 

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