A Combinatoric Probability Question

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In summary, the conversation discusses the probability of finding a set of n consecutive boxes with k or more non-empty boxes when randomly choosing m boxes from an infinite number of boxes. A recursive formula is proposed for calculating this probability using the inclusion-exclusion principle.
  • #1
chingkui
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Suppose we have infinitely many boxes and the probability of anyone box is non-empty is p.
Now if we randomly choose m boxes from them, line them up and name them as box 1, box 2,..., box m. Then for given n and k (k<n<m), what is the probability that there exist a set of n consecutive boxes that we can find k or more non-empty boxes in it?
Anyone know how to approach this question? Thanks.
 
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  • #2
let E(r) be the probaility that there are k empty boxes in the range (r,r+n-1) where r can go from 1 to m-n+1. Then we want to know

P(E(1)or(E(2)or..E(m-n+1))

which is inclusion exclusion principle innit?
 
  • #3
you can formulate the following recursion
f(m+1,n,k)=f(m,n,k)-f(m-n+1,n,k).C(n-1,k-1).p^k.(1-p)^(n-k)
where f(m,n,k) is the probability that...("what you have stated")
 

1. What is combinatoric probability?

Combinatoric probability is a branch of mathematics that deals with counting the number of ways certain events can occur in a given situation.

2. How is combinatoric probability different from regular probability?

Combinatoric probability focuses on the number of outcomes that are possible, while regular probability deals with the likelihood of a specific outcome occurring.

3. What is the formula for calculating combinatoric probability?

The formula for calculating combinatoric probability is nCr = n! / r!(n-r)!, where n is the total number of items and r is the number of items being selected.

4. Can you give an example of a combinatoric probability problem?

Sure, a common example is the probability of rolling a specific number on a die. The combinatoric probability would be 1/6, since there is only one way to roll a specific number out of the six possible outcomes.

5. How is combinatoric probability used in real life?

Combinatoric probability is used in various fields such as statistics, computer science, and economics. It is used to analyze and predict outcomes in situations where there are multiple possible outcomes, such as in games of chance, genetics, and market research.

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