Question 1105708: a bag contains 2 white and 3 black balls. Four persons A,B,C and D in the order
named above, each draw a ball and does not replace it. The person who draws a
white ball first receives Rs. 10. What are their respective expectations?
Answer by Edwin McCravy(20063)   (Show Source):
You can put this solution on YOUR website!
Case 1: A draws a white ball and wins with probability 2/5 = 0.4
Expectation = (0.4)(10) = Rs. 4
Case 2: A draws a black ball and B draws a white ball and
wins with probability (3/5)(2/4) = 3/10 = 0.3
Expectation = (0.3)(10) = Rs. 3
Case 3: A draws a black ball, B draws a black ball, C draws
a white ball and wins with probability (3/5)(2/4)(2/3)
= 1/5 = 0.2
Expectation = (0.2)(10) = Rs. 2
Case 4: A draws a black ball, B draws a black ball, C draws
a black ball and D draws a white ball and wins with
probability (3/5)(2/4)(1/3)(2/2) = 1/10 = 0.1
Expectation = (0.1)(10) = Rs. 1
Edwin
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