What is the Probability of Grouping All Red Marbles Together?

  • MHB
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In summary, the problem involves dividing 36 marbles into 3 groups of 12 and finding the probability that one group will contain all 4 red marbles. This can be approached as a partitioning problem or by considering different cases of choosing red marbles and non-red marbles. The probabilities of each case can be calculated and added to find the overall probability.
  • #1
sscs
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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?
 
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  • #2
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?
 
  • #3
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.
 

FAQ: What is the Probability of Grouping All Red Marbles Together?

What is basic probability?

Basic probability is a branch of mathematics that deals with the likelihood of an event occurring. It is used to calculate the chances of different outcomes in a given situation.

How do you calculate basic probability?

Basic probability is calculated by dividing the number of desired outcomes by the total number of possible outcomes. This gives a decimal value, which can be converted to a percentage to represent the probability.

What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability, on the other hand, is based on actual observations and may vary from the theoretical probability.

What is the probability of selecting a red marble from a bag of marbles?

The probability of selecting a red marble depends on the number of red marbles and the total number of marbles in the bag. For example, if there are 5 red marbles and 20 total marbles, the probability would be 5/20 or 1/4.

How do you account for replacement when calculating probability?

If the marbles are being replaced after each selection, the probability remains the same for each selection. This is known as independent events. If the marbles are not being replaced, the probability would change as the number of marbles decreases. This is known as dependent events.

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