Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

What is the probability to get $n$ times the same element $k$ choosing randomly from a set $A$ knowing the cardinality $|A| = c$?

Thank you in advance,
rubik

share|improve this question
add comment

2 Answers 2

up vote 2 down vote accepted

It depends: is $k$ fixed in advance? if so then the probability is given by $\frac{1}{c^n}$. If you just ask for the probability to have $n$ times the same element, then it is $\frac{1}{c^{n-1}}$ (since the first time you can have any object). By the way, I supposed you are doing exactly $n$ tries. Of course, the probability changes if you are doing more than $n$ tries.

share|improve this answer
    
Thank you! But why does it change if $k$ is fixed? –  rubik Nov 2 '10 at 15:33
    
@rubik: if $k$ is fixed IN ADVANCE, then the first time you must choose it. If $k$ is not decided in advance, then you just ask that starting from the second draw you get the same object as the first time. Thus, the first draw can be anyting. –  Djaian Nov 2 '10 at 15:38
    
Ok, thank you again! –  rubik Nov 2 '10 at 16:51
add comment

Assuming that you draw $n$ times uniformly at random from the set of $c$ elements, it is $\frac{1}{c^{n-1}}$ as Djaian says. You are rolling a $c$-sided die.

share|improve this answer
    
Thank you! I have accepted Djaian's answer because he answered first. Thank you anyway. –  rubik Nov 2 '10 at 15:32
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.