SOLUTION: Ruth and William each have a bag that contains one ball each of the colors yellow, black, green, pink, white, blue and orange. Ruth randomly selects a ball from her bag and puts it

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Ruth and William each have a bag that contains one ball each of the colors yellow, black, green, pink, white, blue and orange. Ruth randomly selects a ball from her bag and puts it      Log On


   

Question 1112244: Ruth and William each have a bag that contains one ball each of the colors yellow, black, green, pink, white, blue and orange. Ruth randomly selects a ball from her bag and puts it in William's bag. Then William randomly selects a ball from his bag and puts it in Ruth's bag. What is the probability that after this the contents of the bag are the same as before?
Answer by ikleyn(52824) About Me  (Show Source):
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To restore the original content, William should take one of the two same color balls from the Ruth's bag.


He can do it by two ways (select one of the two) having 7+1 = 8 options at all.


So, the probability under the question is 2%2F8 = 1%2F4 = 0.25 = 25%.


Notice that this probability does not depends on which ball (which color) will Ruth select.