Solve the given problem involving conditional probability

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Homework Help Overview

The discussion revolves around a problem involving conditional probability related to two boxes containing balls of different colors. Participants explore the probabilities of drawing white balls from one box based on the color of a ball drawn from another box, with specific attention to the implications of the number of balls in each box.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss various methods to approach the problem, including the use of probability trees and conditional probability formulas. There are attempts to clarify the relationships between the probabilities of drawing different colored balls from the boxes, and questions about the implications of specific values for n.

Discussion Status

The discussion is ongoing, with participants providing insights into the calculations and exploring different scenarios. Some participants have suggested alternative methods and questioned the assumptions regarding the number of balls in each box, while others are working through specific cases to identify patterns.

Contextual Notes

There is a noted assumption that n must be greater than or equal to 4, and participants are examining how this affects the calculations. The implications of drawing a black ball from box X are also being considered in relation to the probabilities of drawing a white ball from box Y.

  • #31
Ehm, not so cheerful here, check your post #18 again, P(W) is the addition of those two.
 
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  • #32
Delta2 said:
Ehm, not so cheerful here, check your post #18 again, P(W) is the addition of those two.
Yes, i am aware that ##P(W)= \dfrac{4n-3}{n(n+1)}## is the addition given by

##P(X=B,Y=W) = \dfrac{3}{n} × \dfrac{3}{n+1}= \dfrac{9}{n(n+1)}##

and##P(X=W,Y=W) = \dfrac{n-3}{n} × \dfrac{4}{n+1}= \dfrac{4(n-3)}{n(n+1)}##

My post ##30## is correct.
 
  • #33
yes ok right, it is ##4n-3## there i thought you had ##4(n-3)##.
 
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