web analytics

 Ex 13.1, 10 - A black, red dice (a) Find conditional probability - Conditional Probability - Statement

Slide28.JPG
Slide29.JPG Slide30.JPG

  1. Chapter 13 Class 12 Probability
  2. Serial order wise
Ask Download

Transcript

Ex 13.1, 10 A black and a red dice are rolled. (a) Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5. A black and a red dice are rolled Let us take first numbers to have been appeared on the black die and the second numbers on the red die, in order. S = {(1,1), ……….., (1,6), (2,1), ………, (2,6), (3,1), ………., (3,6), (4,1), ……...., (4,6), (5,1), …….., (5,6), (6,1), …..…., (6,6)} We need to find the probability of obtaining a sum greater than 9, given that the black die resulted in 5 F : 5 appeared on the black die E: Sum of numbers greater than 4 We need to find P(E|F) Also, E ∩ F = {(5,5), (5,6)} So, P(E ∩ F) = 2﷮36﷯ = 1﷮18﷯ P(E|F) = 𝑃(𝐸 ∩ 𝐹)﷮𝑃(𝐹)﷯ = 2﷮36﷯﷮ 6﷮36﷯﷯ = 2﷮6﷯ = 1﷮3﷯ ∴ Required probability is 1﷮3﷯ Ex 13.1, 10 A black and a red dice are rolled. (b) Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4. We need to find the probability of obtaining the sum 8, given that the red die resulted in a number less than 4 F : number on red die is less than 4 E : sum of numbers is 8 We need to find P(E|F) Also, E ∩ F = {(5, 3), (6, 2)} So, P(E ∩ F) = 2﷮36﷯ P(E|F) = 𝑃(𝐸 ∩ 𝐹)﷮𝑃(𝐹)﷯ = 2﷮36﷯﷮ 18﷮36﷯﷯ = 2﷮18﷯ = 𝟏﷮𝟗﷯ ∴ Required probability is 1﷮9﷯

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
Jail