What is the Probability of Grouping All Red Marbles Together?

  • Context: MHB 
  • Thread starter Thread starter sscs
  • Start date Start date
Click For Summary
SUMMARY

The discussion focuses on calculating the probability of grouping all four red marbles together when dividing 36 marbles (32 green and 4 red) into three groups of 12. The problem is approached as a partitioning problem, where the number of ways to partition the red marbles into groups is analyzed. Key cases include selecting all four red marbles in one group and scenarios where red marbles are excluded from the selection. The final probability is determined by summing the probabilities of these distinct cases.

PREREQUISITES
  • Understanding of basic probability concepts
  • Familiarity with combinatorial partitioning
  • Knowledge of binomial coefficients
  • Ability to calculate probabilities of independent events
NEXT STEPS
  • Study combinatorial methods in probability theory
  • Learn about binomial coefficients and their applications
  • Explore partitioning problems in probability
  • Investigate advanced probability techniques, such as conditional probability
USEFUL FOR

Students studying probability, mathematicians interested in combinatorial problems, educators teaching probability concepts, and anyone looking to deepen their understanding of partitioning in probability theory.

sscs
Messages
1
Reaction score
0
I need help starting the following problem. :confused:

There are (36) marbles in a bag-(32) are green and (4) are red. The marbles are to be divided equally into (3) groups of (12). What is the probability that one of the groups will contain all of the (4) red marbles?
 
Physics news on Phys.org
Re: Basic Probability

I would look at this as a partitioning problem. How many ways can we partition 4 objects into 3 groups (2 partitions with 5 potential positions), and how many of those ways have all four objects in one group?
 
Re: Basic Probability

Or another way to think of it is you're "choosing" 12 marbles out of a bag at random. There are a few separate cases you have to consider:

Case #1: Choosing all 4 red marbles out of the bag at once.
Case #2a: Not choosing any red marbles out of the bag, and choosing another 12 marbles, with all 4 of the red marbles in that group.
Case #2b: Not choosing any red marbles out of the bag, then choosing another 12 marbles and not getting any red marbles out of that either.

Find the probabilities of each of these cases and then add them.
 

Similar threads

Probability Word Problem: Aptitude Question
  • · Replies 8 ·
Replies
8
Views
2K
MHB Could use help, know the answers but with the process and equations
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Solve Math Problem: Add Red Marbles for 60% Red
  • · Replies 8 ·
Replies
8
Views
2K
MHB What Is the Probability of Drawing Specific Ball Colors from a Bag?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Probability calculation involving very large numbers
  • · Replies 4 ·
Replies
4
Views
3K
MHB Probability of a particular item not being assigned
  • · Replies 1 ·
Replies
1
Views
2K
High School Relative And Absolute Probability (Probability Of Picking A Red Ball)
  • · Replies 8 ·
Replies
8
Views
3K
MHB Ratio word problem: What fraction of the original counters remain in the bag
  • · Replies 3 ·
Replies
3
Views
2K
What Is the Probability of Drawing a Specific Marble Color Sequence?
  • · Replies 8 ·
Replies
8
Views
8K
Probability of Cheryl Getting 2 Marbles of Same Color
  • · Replies 11 ·
Replies
11
Views
4K