Sample Space of Selecting 5 Balls Without Replacement

In summary, the random experiment involves selecting five balls without replacement from an urn containing six balls numbered 1-6. If the balls are selected simultaneously, there are six different combinations. If they are selected one at a time, the final sample space would be the same as the simultaneous selection method.
  • #1
doozy1414
2
0
Determine the sample space for this random experiment:

An urn contains six balls numbered 1-6. The random experiment consists of selecting five balls without replacement.

The way i did it was by figuring that the balls were selected simultaneously so i got six different combinations. But what if they are selected one at a time?
 
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  • #2
If they were selected one at a time, what would the final sample space be for each possible combination? I'll give you a hint: I don't think what you did and what the answer to the problem is differs so much :)
 
  • #3
Don't post multiple threads for the same topic.
 

1. What is the sample space of selecting 5 balls without replacement?

The sample space of selecting 5 balls without replacement is the set of all possible outcomes when drawing 5 balls from a larger set without replacing any of the balls after each draw. This can be represented as a list of all possible combinations of 5 balls from the original set.

2. How many outcomes are there in the sample space of selecting 5 balls without replacement?

The number of outcomes in the sample space of selecting 5 balls without replacement can be calculated using a combination formula, which is nCr = n! / (r!(n-r)!), where n is the total number of balls in the original set and r is the number of balls being selected. For example, if there are 10 balls in the original set and we are selecting 5 balls, the number of outcomes is 10C5 = 10! / (5!(10-5)!) = 252.

3. What is the probability of selecting a specific combination of 5 balls without replacement?

The probability of selecting a specific combination of 5 balls without replacement can be calculated by dividing the number of ways the specific combination can occur by the total number of outcomes in the sample space. For example, if we want to know the probability of selecting 5 red balls from a set of 10 balls without replacement, the probability would be 10C5 / 10C5 = 1/252.

4. Can the sample space of selecting 5 balls without replacement be visualized?

Yes, the sample space of selecting 5 balls without replacement can be visualized using a tree diagram. The first level of the tree represents the first ball selected, the second level represents the second ball selected, and so on. The branches of the tree represent the different possible outcomes at each level, and the final level of the tree represents the complete sample space of 5 balls.

5. How is the sample space of selecting 5 balls without replacement different from selecting with replacement?

The main difference between selecting 5 balls without replacement and with replacement is that in the former, the number of balls available for selection decreases with each draw, while in the latter, the number of balls available remains the same after each draw. This leads to a larger sample space and different probabilities for each outcome in the without replacement scenario.

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