A bag contains 3 white balls, 3 black balls & 2 red balls. One by one three balls are drawn out without replacement. What is the probability that the third ball is red?
A. 0.25
B. 0.15
C. 0.35
D. 0.45
E. 0.40

• A. 0.25 (or) 1/4 (or) 84/336
  
  There are three cases you can get Red ball in the third pick as follows.
  Cases: 1st Pick -- 2nd Pick -- 3rd Pick
  Case 1: Red -- No Red -- Red
  Case 2: No Red -- Red -- Red
  Case 3: No Red -- No Red -- Red
  
  Case 1:
  Probability of getting red in first pick = 2/8 (out of 3 White + 3 black + 2 red = 8 balls )
  Probability of not getting red in 2nd pick = 6/7 (out of 3 White + 3 black + 1 red = 7 balls)
  Probability of getting red in 3rd pick = 1/6 (out of 3 or 2 White + 2 or 3 black + 1 red = 6 balls)
  Multiplying everything = 12/336
  
  Case 2:
  Probability of getting no red in first pick = 6/8
  Probability of getting red in 2nd pick = 2/7
  Probability of getting red in 3rd pick = 1/6
  Multiplying everything = 12/336
  
  Case 3:
  Probability of not getting red in first pick = 6/8
  Probability of not getting red in 2nd pick = 5/7
  Probability of getting red in 3rd pick = 2/6
  Multiplying everything = 60/336
  
  Summing up all three cases to get 84/336 = 1/4 = 0.25
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