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

[rogo0034]

Homework Statement

Homework Equations

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?

 

[Ray Vickson]

Homework Statement

Homework Equations

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

 

[rogo0034]

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.

 

[Ray Vickson]

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