# Solving Stats Problem: Find Probability of X ≥ 2 after 15 Tries

• rogo0034
In summary: But can't you get the same answers using multiple distributions? ah, i wish there was a info-graphic somewhere i could look at when deciding which distribution a question is looking for to explain the examples. or a flow chart/tree/branch diagram, or w.e it's called.Yes, you can get the same answers using multiple distributions in some cases. However, in this particular problem, the answer is not likely to be the same using multiple distributions.
rogo0034

## The Attempt at a Solution

I've tried putting this into a poisson distribution, binomial, negative binomial. I've tried to get the interval from 0-1 and subtracting that from 1 to find out what the probability is that the Random variable is X ≥ 2 after 15 tries... it just seems like it should be so simple, any ideas?

rogo0034 said:

## The Attempt at a Solution

I've tried putting this into a poisson distribution, binomial, negative binomial. I've tried to get the interval from 0-1 and subtracting that from 1 to find out what the probability is that the Random variable is X ≥ 2 after 15 tries... it just seems like it should be so simple, any ideas?

The first thing you need to decide is WHAT distribution to use: Binomial? Poisson?, some other? Don't guess; look at the original problem, examine what properties each of those distributions correspond to, and decide once and for all which to use. What situation is modeled by the binomial distribution? Does that fit the question? What does the Poisson distribution model? Does it fit the question? Same two questions for the negative binomial.

RGV

But can't you get the same answers using multiple distributions? ah, i wish there was a info-graphic somewhere i could look at when deciding which distribution a question is looking for to explain the examples. or a flow chart/tree/branch diagram, or w.e it's called.

rogo0034 said:
But can't you get the same answers using multiple distributions? ah, i wish there was a info-graphic somewhere i could look at when deciding which distribution a question is looking for to explain the examples. or a flow chart/tree/branch diagram, or w.e it's called.

That is exactly why I suggested that you answer the following questions (repeated here):
"What situation is modeled by the binomial distribution? Does that fit the question? What does the Poisson distribution model? Does it fit the question? Same two questions for the negative binomial."

As to your question about getting the same answers using different distributions: it depends on the problem. In this problem, the answer is: I don't think so. Remember, however, that you might be able to use either the binomial or the Poisson to get nearly the same answer in some cases, because in some cases the Poisson is a *good approximation* to the binomial---although not exactly equal to it.

RGV

## 1. What is the significance of finding the probability of X ≥ 2 after 15 tries?

The probability of X ≥ 2 after 15 tries is a measure of how likely it is for an event to occur at least twice out of 15 trials. This can be useful in various fields such as quality control, finance, and risk assessment, where it is important to know the likelihood of certain outcomes.

## 2. How is this probability calculated?

This probability is calculated using the binomial distribution formula, which takes into account the number of trials, the probability of success, and the number of successes needed. In this case, the number of trials is 15, the probability of success is unknown, and the number of successes needed is 2 or more.

## 3. Can this probability be influenced by external factors?

Yes, the probability can be influenced by external factors such as the accuracy of the data, the assumptions made in the calculations, and the randomness of the events being studied. It is important to carefully consider these factors when interpreting the results.

## 4. What does a higher probability of X ≥ 2 after 15 tries indicate?

A higher probability of X ≥ 2 after 15 tries indicates that it is more likely for the event to occur at least twice out of 15 trials. This could mean that the event is relatively common or that there is a high likelihood of success. It can also suggest that the sample size (15 trials) is large enough to accurately represent the population.

## 5. Is this probability always accurate?

No, the calculated probability is an estimate based on the given data and assumptions. It is not a guarantee of what will happen in reality. However, with a larger sample size and accurate data, the probability can be a good representation of the actual likelihood of the event occurring.

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