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.

Two random 3000 bit arrays each with exactly two ones(1), what is the probability that they have atleast one bit in common?

share|improve this question

2 Answers 2

There are $3000\choose 2$ possibilities for the second array, among these are $2998\choose 2$ that do not have a bit in common with the first. Thus the probabilitiy is $$1- \frac{2998\choose 2}{3000\choose 2}=1-\frac{2998\cdot2997}{3000\cdot2999}.$$

share|improve this answer
    
the approximate answer that should come is 1/500 but i am not getting..how to get that –  Jannat Arora Nov 8 '12 at 17:25
    
@Jannat: It isn’t very close to $1$ in $500$; it’s about $2/3$ in $500$. –  Brian M. Scott Nov 8 '12 at 17:27

It’s easiest here to calculate the probability that they have no $1$’s in common and subtract from $1$. There are $\binom{3000}2$ such arrays. No matter what the first array is, there are $\binom{2998}2$ that have no $1$’s in common with it. Thus, the probability of having no $1$’s in common is

$$\frac{\binom{2998}2}{\binom{3000}2}=\frac{2998\cdot2997}{3000\cdot2999}\approx0.998667\;,$$

and the probability of having at least one $1$ in common is about $0.001333$.

share|improve this answer

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.