Question

A bag contains 5 red balls, 3 blue balls and 4 yellow balls. Two balls are drawn at random one after the other without replacement.

1. Draw a tree diagram to illustrate his pickings. 
2. Calculate the probability that
   • Both balls picked were red. 
   • Both balls picked were of the same colour. 
   • There was no red ball from the two balls picked. 

Answer 1

1.   
   
2.    
   • 1st picking red: ⁵/₁₂
     2nd picking with no replacement: ⁴/₁₁
     red and red= ⁵/₁₂ x ⁴/₁₁= ²⁰/₁₃₂=⁵/₃₃
      
   • r and r  - ⁵/₃₃
     y and y - ⁴/₁₂ x ³/₁₁= ¹²/₁₃₂ =¹/₁₁
     b and b - ³/₁₂ x ²/₁₁= ⁶/₁₃₂= ¹/₂₂
     ⁵/₃₃ + ¹/₁₁ + ¹/₂₂
     10+6+3=19
       66          66
      
   • No red: 
     y and y - ⁴/₁₂ x ³/₁₁= ¹²/₁₃₂
     y and b - ⁴/₁₂ x ³/₁₁= ¹²/₁₃₂
     b and y - ³/₁₂ x ⁴/₁₁= ¹²/₁₃₂
     b and b - ³/₁₂ x ²/₁₁= ⁶/₁₃₂
     =⁴²/₁₃₂= ⁷/₂₂