SOLUTION: An urn contains 3 red balls, 2 white balls and 1 blue ball. Two balls are drawn without replacement. Let A be the event that at least one ball is red, and B be the event that 2 bal

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Question 1183446: An urn contains 3 red balls, 2 white balls and 1 blue ball. Two balls are drawn without replacement. Let A be the event that at least one ball is red, and B be the event that 2 balls are of different colours.
What is p(A)?
What is p(A|B)
Are events A and B independent?
Found 2 solutions by ikleyn, robertb:
Answer by ikleyn(52879)   (Show Source): You can put this solution on YOUR website!
.
An urn contains 3 red balls, 2 white balls and 1 blue ball. Two balls are drawn without replacement.
Let A be the event that at least one ball is red, and B be the event that 2 balls are of different colours.
(a) What is p(A)?
(b) What is p(A|B)
(c) Are events A and B independent?
~~~~~~~~~~~~ 

(a)  Event A is this set of outcomes  { (R,W), (W,R), (R,B), (B,R), (R,R) }.


         P(A) =  = 


              =  =  = .



(b)  Event B is this set  { (R,W), (W,R), (R,B), (B,R), (W,B), (B,W) }.


         P(B) =  = 


              =  =  = .



     The intersection (A and B) is this set  { (R,W), (W,R), (R,B), (B,R) }.


     P(A and B) =  = 


              =  =  = .


     THEREFORE,  P(A|B) =  =  =  = .    ANSWER



(c)  To answer last question, check if P(A and B) is equal to P(A)*P(B).

Solved.



Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!


==>



==> P(A|B) =
Since , A and B are not independent events.
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