Question

A bag contains 8 red, 3 white and 9 blue balls. If three balls are drawn at random, determine the probability that 

(i) all the three balls are blue balls 9

ii) all the balls are of different colours

Answer 1

given: bag which contains 8 red, 3 white, 9 blue balls

Formula: P(E) = \(\frac{favorable\ outcomes}{total\ possible\ outcomes}\) 

three balls are drawn at random therefore

total possible outcomes of selecting two persons is ²⁰C₃

therefore n(S)=²⁰C₃ = 1140

(i) let E be the event that all the balls are blue 

E= {B, B, B} 

n(E)= ⁹C₃ = 84

P(E) = \(\frac{n(E)}{n(S)}\)

P(E) = \(\frac{84}{1140}=\frac{7}{95}\) 

(ii) let E be the event that all balls are of different colour 

E= {B W R} 

n(E)= ⁸C₁ ³C₁ ⁹C₁ = 216

P(E) = \(\frac{n(E)}{n(S)}\)

P(E) = \(\frac{216}{1140}=\frac{18}{95}\)