SOLUTION: A bag contains 2 white balls and 3 black balls, 4 person w,x,y,z in the order named each drawn one ball and not replace it. The first drawn a white ball and received $200, determin

Question 1015108: A bag contains 2 white balls and 3 black balls, 4 person w,x,y,z in the order named each drawn one ball and not replace it. The first drawn a white ball and received $200, determine their expectations.
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
A bag contains 2 white balls and 3 black balls, 4 person w,x,y,z in the order named each drawn one ball and not replace it. The first drawn a white ball and received $200, determine their expectations.

Solution:
Since the balls are not replaced, their expectations are all different.
The expectation of w is that he draws a white ball on the first draw, or
E(w)=P(w)*200=;
The expectation of x winning is if w draws a black AND x draws a white, or
E(x)=P(x)*200=;
Similarly, the expectation of y winning is
E(y)=P(y)*200=;
Finally, if w, x and y all drew a black ball, the remaining balls are white!
E(z)=P(z)*200=;

Check:
E(w)+E(x)+E(y)+E(z)= ..... ok

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