Q:
      
      
         
            
Two boxes contain 4 and 16 balls respectively. Two balls in the first box and four in the second, are black. If a box is chosen randomly and two balls are drawn at random from it, what is the
probability that at least one ball is black if the ball is not replaced?
         
       
      
      
      
          
      
      
          Answer & Explanation
         Answer: C) 77/120         
         
Explanation: At least one black can be chosen in two ways from each box:
Now, probability of choosing at least one black ball from first box 
= 1/2 × [ (2C1× 2C1)/4C2 + 2C2/ 4C2 ]= 5/12
Probability of choosing at least one black ball from 2nd box
= 1/2 × [(4C1×12C1)/16C2 + 4C2/ 16C2] = 9/40
Final probability
= 5/12 + 9/40 = (50 + 27)/120 = 77/120
       
      
      
      
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