Misc 5 - Out of 100 students, two sections of 40, 60 are formed - Using combination

Slide17.JPG
Slide18.JPG

Slide19.JPG

  1. Chapter 16 Class 11 Probability
  2. Serial order wise
Ask Download

Transcript

Misc 5 Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that • you both enter the same sections? n(S) = 100C40, n(A) = 98C38 P(A) = 𝑛(𝐴)﷮𝑛(𝑆)﷯ = 𝟗𝟖𝑪𝟑𝟖﷮𝟏𝟎𝟎𝑪𝟒𝟎﷯ = 98C38 ÷ 100C40 = 98!﷮38! 98 −38﷯!﷯ × 100!﷮40! 100 − 40﷯!﷯ = 98!﷮38!60!﷯ ÷ 100!﷮40!60!﷯ = 98!﷮38!60!﷯ × 40!60!﷮100!﷯ = 98! × 40! × 60!﷮38! × 60! × 100!﷯ = 40 × 39﷮100 × 99﷯ Probability that two students enter same section = Probability that both enter Section A + Probability that both enter Section B = P(A) + P(B) = 40 × 39﷮100 × 99﷯ + 60 × 59﷮100 × 99﷯ = 1560﷮9900﷯ + 3540﷮9900﷯ = 156﷮990﷯ + 354﷮990﷯ = 156 + 354﷮990﷯ = 510﷮990﷯ = 51﷮99﷯ = 𝟏𝟕﷮𝟑𝟑﷯ Misc 5 Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that (b) you both enter the different sections? Probability that they enter different section = 1 – Probability that both enter in same section = 1 – 17﷮33﷯ = 33 − 17﷮33﷯ = 𝟏𝟔﷮𝟑𝟑﷯

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 has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.