# Binomial Probability Distribution

1. Feb 17, 2010

### luv2learn

1. The problem statement, all variables and given/known data
The rejection rate of a certain journal is 45%. If the journal accepts articles at random, what is the minimum number of articles someone has to submit to have a probability of more than 0.75 of getting at least one article accepted?

2. Relevant equations
I'm almost sure this is a binomial distribution question where you take p and n to kook up the P(X) in the binomial probabilities table. Only thing is, I don't know what is n.

3. The attempt at a solution
p=1-0.45=0.55

P(1) = 1-P(X<=0)
>0.75 = 1-P(X<=0)
P(X<=0) < 0.25

But then what? Is my potential n the minimum nr of articles or 1?

{{Also, this is my first post, would someone please tell me where to get the scientific notation for the formulas to put in the posts? Pls and tx! }}}

2. Feb 17, 2010

### tiny-tim

Welcome to PF!

Hi luv2learn! Welcome to PF!

(have an leq: ≤ )

No, it's not binomial …

you're right (if I'm reading you properly: your notation is a bit weird ) that the question is the same as what is 1 - Qn,

where Qn is the probability that all n articles are rejected.

ok, rejections are independent, so what is Qn ?

3. Feb 17, 2010

### luv2learn

Ok, so apparently I've got this whole question wrong, LOL

So the probability that n artiles are rejected is Qn = 0.45 x n

4. Feb 17, 2010

### tiny-tim

erm … with n = 3, that's greater than 1 !

Try again!

5. Feb 17, 2010

### luv2learn

(I'm really losing it, been at it for 10hrs.)

Qn=0.45n ;
Rejecting 1 is: Q1=0.451; Which implies accepting n-1, which is = 1-0.451 = 0.55
Q2=0.452; accept n-2 = 1-0.452 = 0.798; etc.

So if x = minimum nr of articles to be submitted, then I'm actually trying to find
Accept n-x = 1-0.45x > 0.75 ???

6. Feb 17, 2010

### tiny-tim

Now you're confusing me

you're looking for n such that 0.45n < 0.25

(either use logs or just trial-and-error! )

7. Feb 17, 2010

### luv2learn

Yeah, tx. I got the same thing but in a very long (and confusing) way.
In the end n > 1.74 i.e. n = 2

Tx a lot. But is there a simple way of seeing if its a binomial distribution or not? I thought I know but clearly I don't. Or can the same answer be reached if I use binomial distribution probability rules?

8. Feb 17, 2010

### tiny-tim

(How did you get 1.74? )

You're misunderstanding which bit of the binomial is which.

For (p + q)n, the figure for k successes is pkqn-k nCk

in this case, technically, you did use the binomial theorem, but with k = n and therefore nCk = 1.

9. Feb 17, 2010

### luv2learn

0.45n>0.25
log (0.45n>log (0.25)
nlog(0.45)>log(0.25)
n=log0.25/log0.45
n=1.736

10. Feb 17, 2010

### tiny-tim

oh yes, that's fine.