Question 1163319: You are given two urns, each containing a collection of coloured balls. Urn 1 contains three white and two blue balls. Urn 2 contains four white and three blue balls. A ball is drawn at random from urn 1 and put into urn 2. A ball is then picked a random from Urn 2.
What is the probability that the ball picked is white? Assume balls picked from an urn are equally likely to be any of the balls present.
Answer by ikleyn(52790)   (Show Source):
You can put this solution on YOUR website! .
You are given two urns, each containing a collection of coloured balls.
Urn 1 contains three white and two blue balls.
Urn 2 contains four white and three blue balls.
A ball is drawn at random from urn 1 and put into urn 2.
A ball is then picked a random from Urn 2.
What is the probability that the ball picked is white? Assume balls picked from an urn are equally likely to be any of the balls present.
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(1) Analyzing the first step, when we draw the ball from Urn 1 and put it into Urn 2:
After the first step, we draw the white ball from Urn 1 with the probability of  =  and put it into Urn 2.
So, with the probability we get the content (5white,3blue) in the Urn 2 at this step.
Alternatively, with the complement probability  we get the content (4white,4blue) in Urn 2 at this step.
(2) Analyzing the second step, when we draw a ball from Urn 2, we have two respective alternatives
we draw a white ball from Urn 2 (5w,3b) with the probability  =  , or
we draw a white ball from Urn 2 (4w,4b) with the probability  =  .
(3) Now the probability to have finally a white ball from Urn 2 is
P =  +  =  +  =  . ANSWER
Solved.
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