Question

A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that one is red, one is white and one is blue

Answer 1

Given: 6 red, 4 white and 8 blue balls

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

three balls are drawn so, we have to find the probability that one is red, one is white and one is blue total number of outcomes for drawing 3 balls are ¹⁸C₃ 

Therefore n(S)= ¹⁸C₃ = 816 

Let E be the event that one red, one white and one blue ball is drawn 

n(E)= ⁶C₁ ⁴C₁ ⁸C₁ = 192

P(E) = \(\frac{n(E)}{n(S)}\)

P(E) = \(\frac{192}{816}\) = \(\frac{4}{17}\)