Question 1183784
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You will learn nothing, and we will waste a lot of our time, if we work this whole series of related problems for you.  All the concepts involved are basic -- you just need to do the work.<br>
There are 2 choices for which basket to choose first;
there are 2 choices for the color of ball to choose from that basket;
there are 2 choices for which basket to put that ball into; and
there are 2 choices for the color of ball to choose from that second basket<br>
So the number of cases you need to consider is 2*2*2*2=16.<br>
I'll do one of them for you: "1,B,4,W" = choose basket 1; select a black from it; put it in basket 4; select a white from basket 4.  The probability is<br>
P(choose basket 1) = 1/2
P(choose black from basket 1) = 2/5
P(put the black ball in basket 4) = 1/2
P(choose a white from basket 4) = 2/7<br>
The probability for this case is then (1/2)(2/5)(1/2)(2/7) = 1/35.<br>
Calculate the probabilities for each of the other 15 cases.  That will give you the answers for parts a, b, and e.<br>
Note you can check your calculations by verifying that the sum of the probabilities for all 16 cases is 1.<br>
For parts c and d, you are dealing with conditional probability. For an example, the answer for part c is<br><pre>

      P(2nd ball is white and it was drawn from basket 4)
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P(2nd ball is white and it came from either basket 3 or basket 4)</pre><br>
That calculation will be easy since you will have the probabilities for all 16 cases.<br>