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Two identical bags A and B contained identical balls. Bag A has 5 yellow balls and 2 red balls. Bag B has 4 yellow balls and 3 red balls. Two balls are drawn from each bag without replacement.

  1. Draw a tree diagram to illustrate the above information  
  2. Find the probability that;
    1. Both balls are yellow  
    2. The first ball is red and the second yellow   
    3. A red and yellow balls are picked  
    4. At least one ball is red  

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    1. Both balls are yellow
      P(AYY) or P(BYY)
      (½ × 5/7 × 4/6) = (½ × 4/7 × 3/6)
      5/12 + 1/7 = 8/21
    2. First ball is red, second ball yellow
      P(ARY) or P(BRY)
      (½ × 2/7 × 5/6) + (½ × 3/7 × 4/6)
      5/42 + 1/7 = 11/42
    3. P(AYR) or P(ARY) or P(BYR) or P(BRY)
      (½ × 5/7 × 2/6) + (½ × 2/7 × 5/6) + (½ × 4/7 × 3/6) + (½ × 3/7 × 4/6)
      5/42 + 5/42 + 1/7 + 1/7 = 11/21
    4. At least one ball is red
      P(AYR) or P(ARY) or P(BYR) or P(BRY) or P(ARR) or P(BRR)
      (½ × 5/7 × 2/6) + (½ × 2/7 × 5/6) + (½ × 4/7 × 3/6) + (½ × 3/7 × 4/6) + (½ × 2/7 × 1/6)+(½ × 3/7 × 2/6)
      5/42 + 5/42 + 1/7 + 1/7 + 1/42 + 1/14 =13/21
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