MHB Find the probability that each group has an equal amount of odd and even numbers

AI Thread Summary
The discussion focuses on calculating the probability of specific outcomes when dividing a set of numbers from 1 to 4N into two equal groups. Participants seek to determine the likelihood that each group contains an equal number of odd and even numbers, as well as the distribution of numbers divisible by N. There is a request for clarification on the sequence of numbers, indicating a need for a more detailed explanation of the set. The conversation highlights the complexities involved in probability calculations related to group distributions. Overall, the thread emphasizes the importance of clear definitions in mathematical discussions.
Mehrudin
Messages
3
Reaction score
0
A set of numbers 1,2,...,4N gets randomly divided into two groups with equal amount of numbers. Calculate the probability:7
a) Each group has an equal amount of odd and even numbers,
b) All numbers that are divisible by N, to fall in only one of the groups,
c) All numbers that are divisible by N, to be divided equally in the two groups.
 
Mathematics news on Phys.org
It's unclear, at least to me, what the sequence noted as 1, 2, ..., 4N is. You need to give a better description. What is intended?
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
Back
Top