Probability of randomly selecting three big blue marbles?

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Homework Help Overview

The problem involves calculating the probability of randomly selecting three big blue marbles from a bag containing blue, red, and green marbles, with specific counts for each color and size. The context is probability theory, particularly focusing on conditional probabilities and combinations without replacement.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss different methods for calculating the probability, including the use of conditional probabilities and the impact of drawing without replacement. Questions arise about the correct formulation of probabilities for each selection and whether additional divisions are necessary in the calculations.

Discussion Status

The discussion has seen various attempts at calculating the probability, with some participants questioning the necessity of dividing by another number after multiplying probabilities. There is a recognition of the complexity involved in the calculations, and some participants express uncertainty about the correctness of their approaches.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may impose specific formats or methods for presenting their answers. There is also a mention of answer choices provided in a worksheet, which influences the discussion.

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Homework Statement



A bag contains 40 blue marbles, 40 red marbles, 20 green marbles. 60 of the marbles are big. Three marbles are selected without replacement.

What is the probability of randomly selecting three big blue marbles?

Homework Equations



p(x,y/theta=p(x)p(y/x)=p(y)p(x/y)

The Attempt at a Solution



(40/60)(39/59)(38/58)/(40/100)(39/99)(38/98)
 
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first being big blue: p1 = (40/60)(60/100)
second: p2 = (39/60)(59/99)
third: p3 = ...

all 3 = p1*p2*p3
... right?
 
wouldn't p2 = (39/59)(59/99) since there is 1 less big marble left?
 
def (thats what i intended), sorry.
p2 = (39/59)(59/99)
 
after multiplying p1*p2*p3 do I need to divide the sum by another number?
 
Why would you think that you need to divide by another number?
 
Because the answer when p1*p2*p3=.061. yet my worksheet has choices of a. .0125, b. .0240, c. .2323, d. .2400
 
well on second thought you are write, it can't be the above.

B=blue, b=big.

P(B)*P(b) is the probability of the marble being big and blue and it initially = 40/100*60/100 since being big and being blue are independent of each other.

So I get 40/100*60/100*39/99*59/99*38/98*58/98 for all 3 to be B&b, since they are drawn in succession and without replacement. That = 0.0129, which is close to A?
 
Thanks I got it and I really appreciate your help!
 
  • #10
so was A the answer? I am just curious.
 
  • #11
yes thanks!
 

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