Hello, flywithme!

You left out part of the problem.

I'll take a guess at what's missing.

This is Conditional Probability, requiring Bayes' Theorem.BagMhas 5 white balls and 2 red balls.

BagNcontains 3 white balls and 4 red balls.

A ball is randomly chosen from BagMand moved to BagN.

If a white ball is selected from BagN, what is the probability

that a red ball was transferred from BagMto BagN?

. . .[1]

We consider the two cases . . .

[1] White moved from Bag M: .

. . Then bag N has 4W, 4R: .

. . Then: .

[2] Red moved from Bad M: .

. . Then Bag N has 3W, 5R: .

. . Then: . .[2]

Hence: . .[3]

Substitute [2] and [3] into [1]: .