Calculating Probability of 3 Pennies in 30 Boxes Using Poisson Distribution

In summary, the conversation discusses using a Poisson distribution with a λ value of 10/3 to calculate the probability of having exactly 3 pennies in box #1 out of 100 pennies distributed randomly into 30 boxes. However, the answer key suggests using a binomial distribution with N = 100, k = 3, and p = 1/30. The conversation then concludes with the clarification that the probability being calculated is for one penny specifically ending up in box #1.
  • #1
little neutrino
40
1
One hundred pennies are being distributed independently and at random into 30 boxes, labeled 1, 2, ..., 30. What is the probability that there are exactly 3 pennies in box number 1?

I tried using a Poisson distribution f(x) = (e^-λ)*(λ^x)/x! , with λ = 100/30 = 10/3 and x = 3. I got 0.22021 (5 s.f.), but the answer key is 0.22345. Am I using the wrong distribution? Thanks!
 
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  • #2
For anyone penny, what is the probability that it will end up in box # 1?
Use a binomial distribution...N = number of pennies. k = 3. p = probability of landing in box #1.
 
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Likes little neutrino
  • #3
RUber said:
For anyone penny, what is the probability that it will end up in box # 1?
Use a binomial distribution...N = number of pennies. k = 3. p = probability of landing in box #1.

Ok I got it! Thanks! :)
 

1. What are discrete distributions?

Discrete distributions are statistical distributions that describe the probability of a specific outcome or set of outcomes occurring in a discrete or countable set of events. They are used to model random variables that can only take on a finite or countably infinite number of values.

2. What is an example of a discrete distribution?

An example of a discrete distribution is the binomial distribution, which models the number of successes in a series of independent trials with a fixed probability of success. Another example is the Poisson distribution, which models the number of occurrences of a rare event in a given time or space.

3. How do you calculate the mean and variance of a discrete distribution?

The mean of a discrete distribution is calculated by multiplying each possible outcome by its corresponding probability and summing the values. The variance is calculated by taking the sum of the squared differences between each outcome and the mean, multiplied by its probability, and then summing these values.

4. What is the difference between discrete and continuous distributions?

The main difference between discrete and continuous distributions is that discrete distributions model variables that can only take on a finite or countably infinite number of values, while continuous distributions model variables that can take on any value within a given range. Discrete distributions are often used for counts or whole numbers, while continuous distributions are used for measurements or real numbers.

5. How are discrete distributions used in practical applications?

Discrete distributions are used in a wide range of practical applications in fields such as finance, engineering, and biology. They can be used to model the number of defects in a manufacturing process, the number of customers in a queue, or the number of mutations in a DNA sequence. They are also used in statistical tests and hypothesis testing to determine the significance of observed data.

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