Question

A bag contains 5 red, 4 white and 3 blue beads. Three beads are selected at random without replacement. Find the probability that

1. The first red bead is the third bead picked. 
2. The beads selected were, white and blue: 
   • In that order
   • In any order 
3. No red bead is picked 
4. Beads picked are of the same colour. 

Answer 1

1. The first red bead is the third bead picked. (2mks)
   P(WWR or WBR or BBR or BWR)
   (⁴/₁₂ X ³/₁₁ X ⁵/₁₀) + ⁴/₁₂ X ³/₁₁ X ⁵/₁₀
   + (³/₁₂ x ²/₁₁ x ⁵/₁₀ + (³/₁₂ x ⁴/₁₁ x ⁵/₁₀))
   = ²/₁₁
2. The beads selected were, white and blue: (2mks)
   • In that order
     ⁵/₁₂ x ⁴/₁₁ x ³/₁₀ = ¹/₂₂
   • In any order 
     P(RWB or RBW or WBR or WRB or BWR or BRW)
     (⁵/₁₂ x ⁴/₁₁ x ³/₁₀) + (⁵/₁₂ x ³/₁₁ X ⁴/₁₀)
     + (⁴/₁₂ x ³/₁₁ x ⁵/₁₀)
     = ⁶/₅₂ = ³/₁₁
3. No red bead is picked 
   P(BBB or BBW or BWB or BWW or WWW or WWB or WBW OR WBB)
   (³/₁₂ x ²/₁₁ x ¹/₁₀)+(³/₁₂x²/₁₁x⁴/₁₀)+(³/₁₂x⁴/₁₁x²/₁₀)+(³/₁₂x⁴/₁₁x³/₁₀ )+
   (⁴/₁₂x³/₁₁x²/₁₀)+(⁴/₁₂x³/₁₁x³/₁₀) +(⁴/₁₂x³/₁₁x²/₁₀)
   =⁷/₄₄
4. Beads picked are of the same colour. 
   P(BBB or WWW or RRR)
   (³/₁₂x²/₁₁x¹/₁₀)+(⁴/₁₂x³/₁₁x²/₁₀)+(⁵/₁₂ x ⁴/₁₁x³/₁₀)
   = ¹/₂₂₀ + ¹/₅₅ + ¹/₅₅ = ⁹/₂₂₀