Expert: Paul Klarreich - 5/31/2008

Question
A container A contains 6 red and 4 green spheres, whereas a second container B contains 7 red and 3 green spheres. A sphere is chosen by luck from container A and it is put at container B. Then, a sphere is chosen by luck from container B and it is put at A. After the end of the experiment find the probability of the events:
(a) To be chosen a red sphere from container A and a red sphere from container B
(b)No to change the composition of the containers, i.e. container A to contain 6 red and 4 green spheres and  container B to contain 7 red and 3 green spheres.

PS: I am mostly interested in part (a). Thanks in advance.

Answer
Questioner:   Yannis
Category:  Advanced Math
Private:  No
 
Subject:  Difficult Probability Question - Urgent
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Hi, Yannis,

I am afraid your question is not clear:

What do you mean by 'and it is put AT container B (or A)'?  

Do you really mean:  'it is put IN container B(or A)'

I suggest this wording for your questions:


Question:  Container A contains 6 red and 4 green balls, and  B contains 7 red and 3 green balls. A ball is DRAWN from A and it is put at (IN?) B. Then a ball is DRAWN from B and it is put at (IN?) A. Find the probability of the events:

(a) To be chosen a red sphere from container A and a red sphere from container B
(a) A red ball was drawn from both A and B.
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I cannot answer as you have written, but ASSUMING THE QUESTION AS FOLLOWS, I'll try:

A contains 6 red and 4 green balls, and  B contains 7 red and 3 green balls. A ball is DRAWN from A and it is put INTO B. Then a ball is DRAWN from B and it is put INTO A. Find the probability of the events:


(a) A red ball was drawn from both A and B.


p(drawing red from A) = 6/10 = 3/5.
If we did, then B now has 8 red and 3 green.  Now:

p(drawing red from B) = 8/11.

p(both) = product = 3/5 * 8/11 = 24/55

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(b)To leave the composition of the A and B just as they are.

Let me know if this is correct and you really need it.  You just have to compute:

p(red from A, red from B) PLUS
p(green from A, green from B)