Question 1072488: Is the binomial distribution appropriate for the following situation?
Joe buys a ticket in his state’s “Pick 3” lottery game every week; X is the number of times in a year that he wins a prize. Can you show step-by-step how you got the answer Plaese
Yes
No
Cannot determine from information given
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i think it might be appropriate.
the answer to the question should be yes.
here's my explanation.
you have either a win or a lose proposition each week.
let p equal the probability of winning.
let q equal the probability of losing.
since this is a win or lose situation, then q = 1 - p.
let x equal the number of times he wins in a year.
let n equal the number of times he plays.
let p(x) equal the probability of winning x times.
the binomial formula is:
p(x) = p^x * q^(n-x) * c(n,x)
we'll assume that the probability of winning is .05.
this is not accurate, but is ok for example purposes because it's simple enough to be shown clearly.
you get p = .05
since q = 1 - p, you get q = .95
we have n = 52.
x will range from 0 to 52.
the formula for p(x) will become:
p(x) = .05^x * .95^(52-x) * c(52,x)
for example:
when x = 0, this formula becomes:
p(0) = .05^0 * .95^52 * c(52,0)
simplify this to get p(0) = .05^0 * .95^52 * 1 which is equal to .06944.....
c(n,x) is the number of ways you can get sets of x items from n items.
c(n,x) is equal to n! / (x! * (n-x)!)
i used excel to calculate all the probabilities, the sum of which is equal to 1, as it should be.
you can see that p(x = 0) is .0694..... as i had calculated manually.
those calculations are shown below:
the requirements for the binomial formula can be found in the following reference.
https://people.richland.edu/james/lecture/m170/ch06-bin.html
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