Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Probability and Recipricals
Name: Safwaan K.
Status: student	
Age:  N/A
Location: N/A
Country: N/A
Date: N/A 


Question:
Hi, I have made a bit of a discovery that i wish to share with you. Could you let me know if this is something new that I have discovered. If it is, I want all the credit :) Law Of Probable Recipricol Division:



Replies:
Bascially, I have found that the probability of selecting any random number which is exactly divisible by itself is exactly equal to the recipricol of that number. That is to say:

The probability that X is exactly divisble by Y is equal to 1/x. or the probability that (X MOD Y = 0) = 1/x for example:

What is the probability that a random number between 1 and 100000000 is divisible by 19? The answer is 1/19 = 0.05263, i.e there is a 5.263% chance that a random number is divisible by 19.

Probability is not really my field, and I have not been able to dis-prove this, but I would simply qualify the original stated example by adding, rather than "between", the words "numbers from 1 to 10,000,000 inclusive". The solution could fall apart if the end values are not included (I suspect).

I note that the white filling of an Oreo cookie lies 'between' the two chocolate wafers but does not include them. If your solution is intended to include the end digits, it is better stated; otherwise, the cookie crumbles. ;)
Thanks for using NEWTON!

Ric Rupnik


I am not sure I find your result a surprise. In the interval between 1 and 100,000,000 which =100x10^6 there 100x10^6 / 19 = 5.2361578... x10^6 multiples of 19. 1x19, 2x19, 3x19, ..., 5.23631578...x10^6x 19 = 100x10^6 give-or-take round off error.

So the probability of randomly choosing a number in the interval between the integers 1 and 100x10^6 that is a multiple of 19 is: the number of multiples of 19 in the interval divided by the number of integers in the interval, or 5.2361578...x10^6 / 100x10^6 = 0.052361578...

Vince Calder



Click here to return to the Mathematics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (help@newton.dep.anl.gov), or at Argonne's Educational Programs

NEWTON AND ASK A SCIENTIST
Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory