We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
259
2
avatar+194 

Bag A has 3 white and 2 black marbles. Bag B has white 4 and black 3 marbles.


Suppose we draw a marble at random from Bag A and put it in Bag B. After doing this, we draw a marble at random from Bag B, which turns out to be white. Given this information, what is the probability that the marble we moved from Bag A to Bag B is white?

___________________________________________________

I got an answer of 103/245, but it was wrong. How do i approach this problem, and if possible, please provide multiple hints, and paybe the solution! Thanks!

 Sep 16, 2018
edited by Max0815  Sep 16, 2018
 #1
avatar+5776 
+2

A = 3W2B

B = 4W3B

 

transfer W from A to B gives: A = 2W2B, B = 5W3B, Probability 3/5

transfer B from A to B gives : A = 3W1B, B = 4W4B, Probability 2/5

 

Let event X be the event that the moved marble was white

Let event Y be the event that the marble chosen from bag B was white

 

We want P[X | Y]

 

\(P[X | Y] = \dfrac{P[Y|X]P[X]}{P[Y]}\)

 

\(P[Y|X] = \dfrac 5 8\\ \\ P[X] = \dfrac 3 5 \\ \\ P[Y] = \dfrac 5 8 \dfrac 3 5 + \dfrac 4 8 \dfrac 2 5 = \dfrac{23}{40}\)

 

\(P[X|Y] = \dfrac{\frac 5 8 \cdot \frac 3 5}{\frac{23}{40}} = \dfrac{15}{23}\)

 Sep 16, 2018
edited by Rom  Sep 16, 2018
edited by Rom  Sep 16, 2018
 #2
avatar+194 
+1

Thank you very much!!!!!!!

 Sep 16, 2018

5 Online Users

avatar