Infinite supply of marbles probability problem

Click For Summary
SUMMARY

The probability problem discussed involves an infinite supply of marbles, where marble number 1 is placed in an urn alongside others in pairs. As the process continues indefinitely, the probability that marble number 1 remains in the urn is calculated as the limit of (n-1)/n as n approaches infinity. The conclusion drawn is that the probability approaches zero, indicating that marble number 1 will not remain in the urn forever. This result is confirmed by the iterative calculations provided, which demonstrate the diminishing likelihood of marble number 1's retention.

PREREQUISITES
  • Understanding of probability theory, particularly concepts of infinite sequences.
  • Familiarity with basic combinatorial principles and random selection.
  • Knowledge of limits and their application in probability calculations.
  • Ability to interpret mathematical notation and sequences.
NEXT STEPS
  • Study the concept of limits in calculus to better understand infinite sequences.
  • Explore advanced probability theory, focusing on random processes and their implications.
  • Investigate combinatorial probability and its applications in real-world scenarios.
  • Learn about stochastic processes and their relevance to infinite supply problems.
USEFUL FOR

Students studying probability theory, mathematicians interested in combinatorial problems, and educators seeking examples of infinite processes in probability discussions.

Roni1985
Messages
200
Reaction score
0

Homework Statement


A has an infinite supply of marbles numbered 1,2,3,... A places the marbles, two at a time and in numerical order, into an urn (i.e. first 1 and 2, then 3 and 4, etc.). Each time A puts two marbles, B reaches in and pulls on out. This process goes on forever.

c) If B always removes marbles randomly (each marble in the urn equally likely to e removed), with what probability will marble number 1 remain in the urn forever?


Homework Equations





The Attempt at a Solution


Here is what I did:
1,2 =>prob that 1 stays is 1/2

1,3,4 => prob that 1 stays is 2/3

1,3,4,6 =>prob that 1 stays is 3/4

until (n-1)/n

so we need to multiply them all and we are left with 1/n
so as n->inf, the probability that it happens is zero ?

Is my answer correct ?

Thanks,
Roni.
 
Physics news on Phys.org


Seems fine to me.
 


Dick said:
Seems fine to me.

I see, thanks very much :)
 

Similar threads

Probability: Infinite marbles placed in, and selected from an urn
  • · Replies 2 ·
Replies
2
Views
2K
Probability Word Problem: Aptitude Question
  • · Replies 8 ·
Replies
8
Views
3K
High School Black and white marbles probability question
  • · Replies 5 ·
Replies
5
Views
3K
What Is the Probability of Drawing a Specific Marble Color Sequence?
  • · Replies 8 ·
Replies
8
Views
8K
Find an exact formula for this problem
  • · Replies 3 ·
Replies
3
Views
2K
Conditional probability problem
  • · Replies 2 ·
Replies
2
Views
3K
Question about conditional probability
  • · Replies 2 ·
Replies
2
Views
2K
What Are the Probability Mass Functions for Randomly Selected Marbles?
  • · Replies 5 ·
Replies
5
Views
3K
Probability, Bag of Marbles - quantity grabbed > quantity needed
  • · Replies 3 ·
Replies
3
Views
3K
How to show that these sequences are summable?
  • · Replies 1 ·
Replies
1
Views
2K