Why Does the Order of Drawing Marbles Affect the Probability Calculation?

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Homework Help Overview

The discussion revolves around probability calculations involving drawing marbles from a jar. The original poster presents a scenario with a jar containing 3 black marbles and 1 red marble, focusing on the probability of drawing a black marble followed by a red marble with replacement. Participants explore the implications of order in probability calculations and the concept of drawing with replacement.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants question why the order of drawing marbles is significant in this context, particularly when the problem specifies drawing two marbles. There is discussion about the meaning of "with replacement" and how it affects the calculations. Some participants also reflect on a similar problem involving drawing without replacement and the differences in probability outcomes.

Discussion Status

The discussion is ongoing, with participants actively questioning assumptions and clarifying the problem's requirements. Some have provided calculations based on their interpretations, while others express confusion about the phrasing of the problems and the expected outcomes.

Contextual Notes

Participants note that the phrasing of the problems may lead to different interpretations, particularly regarding whether the order of drawing matters and how replacement affects the probabilities. There is also mention of a discrepancy between calculated probabilities and expected answers, indicating potential misunderstandings of the problem statements.

DotKite
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Homework Statement



Consider a jar with 3 black marbles and 1 red, for the experiment of drawing two with replacement. What is the probability of drawing a black then a red in that order? Assume all marbles are equally likely to be drawn.

Homework Equations





The Attempt at a Solution


Ok first why do they say "find the probability in that order"? Why does order matter if you are taking two at a time? Then they say assume all marbles are equally likely to be drawn? Uhhhh what?
 
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DotKite said:

Homework Statement



Consider a jar with 3 black marbles and 1 red, for the experiment of drawing two with replacement. What is the probability of drawing a black then a red in that order? Assume all marbles are equally likely to be drawn.

Homework Equations


The Attempt at a Solution


Ok first why do they say "find the probability in that order"? Why does order matter if you are taking two at a time? Then they say assume all marbles are equally likely to be drawn? Uhhhh what?

It matters because that is what they have asked you to do. In some problems the order does not matter, but in this one it does. The problem never said you draw two at the same time; it just said you draw two.
 
Ray Vickson said:
It matters because that is what they have asked you to do. In some problems the order does not matter, but in this one it does. The problem never said you draw two at the same time; it just said you draw two.
Moreover, if it were drawing two at the same time then it would not be 'with replacement'.
 
Ray Vickson said:
It matters because that is what they have asked you to do. In some problems the order does not matter, but in this one it does. The problem never said you draw two at the same time; it just said you draw two.

Oh you are right! Fml
 
Ok the problem is totally easy when you don't read it wrong lol.

So first draw of black is 3/4. Then you replace and the second draw of red is 1/4. So the prob of black then red is 3/16
 
Ok there is a similar question

An urn contains four balls: one red, one green, one yellow, and one white.
Two balls are drawn without replacement from the urn. What is the probability of getting a red ball and a white ball. Ok so for red on the first draw is 1/4. Then for white on second draw we have 1/3. So the probability of red and white is 1/12 right?

Seems right to me but apparently the answer is .167?
 
DotKite said:
Ok there is a similar question

An urn contains four balls: one red, one green, one yellow, and one white.
Two balls are drawn without replacement from the urn. What is the probability of getting a red ball and a white ball.


Ok so for red on the first draw is 1/4. Then for white on second draw we have 1/3. So the probability of red and white is 1/12 right?

Seems right to me but apparently the answer is .167?
It says "a red ball and a white ball", not "a red ball then a white ball".
 

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