Binomial Distrubition/Die rolling Question.

In summary, to find the probability of rolling at least 2 "sixes" in 6 rolls of a balanced die, you can use the Binomial Formula with the probability of success (rolling a six) being 1/6, the number of trials being 6, and the number of successes being 2. This will give you the probability of rolling exactly 2 "sixes." To find the probability of rolling at least 2 "sixes," you can add the probabilities of rolling 2, 3, 4, 5, or 6 "sixes."
  • #1
derek10rr2
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How to Find the Probability of rolling at least 2 "sixes" in 6 rolls of a balanced die.

I am trying to solve using the Binominal Formula, P(X = r) = nCr p r (1-p)n-r

But am not really sure what the probability rates for success and failure should be or how to compute it.

Any advice?

Thanks.
 
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  • #2
derek10rr2 said:
How to Find the Probability of rolling at least 2 "sixes" in 6 rolls of a balanced die.

I am trying to solve using the Binominal Formula, P(X = r) = nCr p r (1-p)n-r

But am not really sure what the probability rates for success and failure should be or how to compute it.

Any advice?

Thanks.

p(S)=1/6 n=6 r=2 I assume in your formula you mean: [tex]p^r (1-p)^{n-r}[/tex]
 
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FAQ: Binomial Distrubition/Die rolling Question.

What is the Binomial Distribution?

The Binomial Distribution is a statistical probability distribution that describes the likelihood of a certain number of successes in a fixed number of independent trials, given a specific probability of success for each trial.

How is the Binomial Distribution related to die rolling?

The Binomial Distribution can be used to model the probability of rolling a specific number on a die, as each roll can be considered an independent trial with a fixed probability of success (rolling the desired number).

What are the characteristics of a Binomial Distribution?

A Binomial Distribution is characterized by the number of trials, the probability of success for each trial, and the number of successes desired. It is also a discrete distribution, meaning the possible outcomes are countable, and the trials are independent of each other.

How is the Binomial Distribution formula calculated?

The formula for the Binomial Distribution is P(x) = (nCx) * (p^x) * (q^(n-x)), where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure (q = 1-p).

What are some real-world applications of the Binomial Distribution?

The Binomial Distribution is commonly used in fields such as finance, marketing, and quality control to model the probability of success or failure in a given situation, such as the success rate of a marketing campaign or the likelihood of a product defect. It is also used in genetics to predict the outcomes of genetic crosses and in sports analytics to analyze player performance and predict game outcomes.

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