Question 1015108
 
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={{{2/5*200=80}}};
The expectation of x winning is if w draws a black AND x draws a white, or 
E(x)=P(x)*200={{{(3/5)*(2/4)*200=3/10*200=60}}};
Similarly, the expectation of y winning is 
E(y)=P(y)*200={{{(3/5)*(2/4)*(2/3)*200=1/5*200=40}}};
Finally, if w, x and y all drew a black ball, the remaining balls are white!
E(z)=P(z)*200={{{(3/5)*(2/4)*(1/3)*1*200=1/10*200=20}}};
 
Check:
E(w)+E(x)+E(y)+E(z)={{{80+60+40+20=200}}} ..... ok