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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.