Question 12 (ii) - End-of-Chapter Exercises - Chapter 7 - The Mathematics of Maybe: Introduction to Probability

Transcript

Question 12 (ii) Write the sample space and calculate the probability based on the given information. (ii) A bag contains 4 red, 3 green, and 2 blue balls. Two balls are drawn without replacement. What is the probability that both are of different colours? Here, the ball is taken out without replacement So, our probabilities when picking second ball needs to be carefully calculated Now, Probability that both are of different colours = Probability it is (Red, Green) + Probability it is (Red, Blue) + Probability it is (Green, Red) + Probability it is (Green, Blue) + Probability it is (Blue, Red) + Probability it is (Blue, Green) = 𝟒/𝟗 ×𝟑/𝟖+𝟒/𝟗 ×𝟐/𝟖+𝟑/𝟗 ×𝟒/𝟖+𝟑/𝟗 ×𝟐/𝟖+𝟐/𝟗 ×𝟒/𝟖+𝟐/𝟗 ×𝟑/𝟖 = (12 + 8 + 12 + 6 + 8 + 6)/72 = 52/72 = 𝟏𝟑/𝟏𝟖