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# Thread: A question about negative binomial distribution

1. ## A question about negative binomial distribution

one quesion form November 2001.
A company takes out insurance policy to cover accidents that occur at its manufacturing plant. The prob. that one or more accidents will occur during any given month is 3/5. The number of accidents that occur in any given month is independent of the number of accidents that occur in all other months.

Calculate the probability that there will be at least four months in which no accidents occur before the fourth month is which at least one accident occurs.

I don't understand the question. thanks for help

2. Originally Posted by Libby
one quesion form November 2001.
A company takes out insurance policy to cover accidents that occur at its manufacturing plant. The prob. that one or more accidents will occur during any given month is 3/5. The number of accidents that occur in any given month is independent of the number of accidents that occur in all other months.

Calculate the probability that there will be at least four months in which no accidents occur before the fourth month is which at least one accident occurs.

I don't understand the question. thanks for help
You need to use the negative binomial distribution which is
f(x)=(x+r-1)choose(x)(p^r)(1-p)^x
where p is the probability of success (i.e. probability of more than one accident in a month), 1-p is the probability of no accidents, r is the number of successes (so 4 months with one or more accidents) and x is the number of months with no accidents. X is the number of failures until the r-th success occurs.

So I believe that the equation should be:
f(4)=(4+4-1)choose(4)(3/5)^4(2/5)^4 = 0.11612

-karen

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