Question

IB exams

A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

Answer 1

2 yellow       3  green      2 blue balls
 
probability that the first ball is blue: 2/(2+3+2) = 2/7

probability that the first ball is not blue = 1 - 2/7 = 5/7
if the first ball is not blue, then we have  4 other colors + 2 blue balls remaining.
     probability that the second ball is blue :  2/(4+2) = 1/3

probability that at least one ball is blue:
    = P(1st ball is blue) + P(first ball is not blue  AND second ball is blue)
    =  2/7  +  5/7 * 1/3  = 11 / 21

probability that none of the balls is blue = 1 - 11/21 = 10/21
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The bag contains 5 non-blue and 2 blue balls.
probability that 1st ball is not blue = 5/7
  If 1st ball is non blue, then there are 4 non-blue and 2 blue balls remaining in the bag.
         then probability that 2nd ball is non blue = 4/6

probability that 1st ball is non-blue  AND  2nd ball is not blue = 5/7 *  4/6 = 10/21