Question 1183784: A ball is randomly drawn from either basket 1 or basket 2. Basket 1 has 3 white balls and 4 black balls. Basket 2 has 2 white and 3 black balls. The drawn ball is then randomly put into either basket 3 or basket 4. Basket 3 has 3 white and 3 black balls. Basket 4 has 2 white and 4 black balls. A ball is then randomly drawn from either basket 3 or basket 4.
a) What is the probability of drawing a white ball in the 2nd attempt?
b) What is the probability of drawing a black ball in the 2nd attempt?
c) If the 2nd ball drawn is white, what is the probability that it came from basket 4?
d) If the 2nd ball drawn is black, what is the probability that it came from basket 1?
e) Which ball draw event is the most likely to happen? The least likely to happen?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
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.
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
So the number of cases you need to consider is 2*2*2*2=16.
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
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
The probability for this case is then (1/2)(2/5)(1/2)(2/7) = 1/35.
Calculate the probabilities for each of the other 15 cases. That will give you the answers for parts a, b, and e.
Note you can check your calculations by verifying that the sum of the probabilities for all 16 cases is 1.
For parts c and d, you are dealing with conditional probability. For an example, the answer for part c is
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)
That calculation will be easy since you will have the probabilities for all 16 cases.
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