Selecting from an Urn. Conditional probability

In summary, the conversation discusses the probability of obtaining 1 red ball and 2 white balls from a sample of 3 balls drawn without replacement from a box containing 4 red balls and 6 white balls. The question specifically asks for the probability given that at least 2 of the balls in the sample are white. The correct answer is 3/4, which can be found by calculating P(W ≥ 2) and P(W = 2).
  • #1
torquerotates
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Homework Statement



A box contains 4 red balls and 6 white balls. A sample size of 3 is drawn without replacement from the box. What is the probability of obtaining 1 red ball and 2 white balls given that at least 2 of the balls in the sample are white?

Homework Equations





The Attempt at a Solution


Well if I got at least two white balls that means that I either have 2W or 3W. If I have 2W, then I can chose among the remaining 4W and 4R. Hence the probability is 1/2 given that i already otained 2W. If i have 3W, the probabilty is 0 given that i already obtained 2W. Hence my answer is 1/2. BUT... I am wrong. the answer is 3/4. I am not sure where i went wrong here.
 
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  • #2
hi torquerotates! :smile:
torquerotates said:
What is the probability of obtaining 1 red ball and 2 white balls given that at least 2 of the balls in the sample are white?
…
If I have 2W, then I can chose …

no, that's if the question says "given that the first 2 of the balls in the sample are white"

(or any particular pair)

find P(W ≥ 2) and P(W = 2) :wink:​
 

1. What is an urn in the context of probability?

An urn is a hypothetical container used in probability theory to represent a collection of objects. It is typically used in situations where we are interested in selecting objects randomly from a given set.

2. What is the conditional probability of selecting an object from an urn?

Conditional probability is the likelihood of selecting an object from an urn given that certain conditions are met. It is calculated by dividing the probability of the desired outcome by the total number of possible outcomes.

3. How do you calculate the probability of selecting a specific object from an urn?

The probability of selecting a specific object from an urn can be calculated by dividing the number of desired outcomes by the total number of possible outcomes. This is known as the "classical" or "a priori" probability.

4. What role does the size of an urn play in selecting objects from it?

The size of an urn can impact the probability of selecting an object from it. A larger urn with more objects will have a lower probability of selecting a specific object compared to a smaller urn with fewer objects. However, the overall probability of selecting an object from the urn will remain the same.

5. How does the concept of independence apply to selecting from an urn?

The concept of independence means that the outcome of one selection does not affect the probability of selecting a specific object in subsequent selections. In the context of selecting from an urn, this means that the probability of selecting a specific object remains the same regardless of previous selections.

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