SOLUTION: A bag contains 2 white balls and 3 black balls each of four persons A,B,C, and D in the order named, drawsone ball and does not replace it, the first to draw a white ball receives

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Question 1028109: A bag contains 2 white balls and 3 black balls each of four persons A,B,C, and D in the order named, drawsone ball and does not replace it, the first to draw a white ball receives $10. Determine the expectation of A,B,C, and D?
Answer by mathmate(429) About Me  (Show Source):
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Question:
A bag contains 2 white balls and 3 black balls each of four persons A,B,C, and D in the order named, drawsone ball and does not replace it, the first to draw a white ball receives $10. Determine the expectation of A,B,C, and D?

Solution:
This problem is best solved using a probability tree, which displays clearly the possible outcomes while saving a lot of bookkeeping.

So in conclusion, the probability as shown in the tree diagram decreases from A to D, in the sequence
{P(A)=4/10, P(B)=3/10, P(C)=2/10, P(D)=1/10}