There are two box,one containing 10 red balls and the other containing 10 green balls. You are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is
a) 3/4
b) 37/38
c) 1/2
d) 14/19

• 14/19
  
  To maximise probability of red ball,
  Move 9 red balls in other box such that one box contains 1 red ball and other box contains 9 red and 10 green balls,
  
  then
  
  probability of getting red ball = 1/2 *1 + 1/2*9/19 = 1/2+9/38= 28/38=14/19
• 14 years agoHelpfull: Yes(120) No(9)
• probability of choosing one box 1/2
  prob of choosing red ball from green ball 1/2
  rest 9/19
  so,1/2+1/2*(9/19)=14/19
• 14 years agoHelpfull: Yes(19) No(2)
• 1/2.
  
  probability of choosing box with red balls is 1/2 and choosing red ball from that box is 1.
  so final probability = 1/2
• 14 years agoHelpfull: Yes(5) No(39)
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• 10 years agoHelpfull: Yes(0) No(0)
• the probability for selecting red box is 1/2 but randomly if we select green box, the probability will be 0.
  so, total probability for this case is 0.5.
  
  now consider the other case, 9 red balls are transferred to green ball box. now total balls in that box will be 19.
  
  total probability = probability to select 1st box + probability to select 2nd box
  
  = (1/2)*(1C1/1C1)+(1/2)*(9C1/19C1)
  
  = (1/2)*(1+9/19)
  
  = (1/2)*(28/19)
  
  = 14/19
• 9 years agoHelpfull: Yes(0) No(0)