Q. Out of 100 students two sections of 40 and 60 students are to be formed. If Jack and Jenny are among the 100 students, what is the probability that: a) they end up in the same section? b) they end up in different sections?
I calculated the answer of the first part just fine, it came out to be: (⁴⁰C₂+⁶⁰C₂)/¹⁰⁰C₂ =17/33
Now, to find the answer to the second part I could subtract the answer of the first part from 1 and get 16/33 which is the answer printed in my exercise book. However I’m in a bit of a dilemma.
If instead of thinking that way I say that there are two possibilities:
- Jack ends up in A and Jenny in B. This would give the answer as: (⁴⁰C₁.⁶⁰C₁)/¹⁰⁰C₂
- Jack ends up in B and Jenny in A. Which would again give the answer as: (⁴⁰C₁.⁶⁰C₁)/¹⁰⁰C₂
so the final answer would be 2(⁴⁰C₁.⁶⁰C₁)/¹⁰⁰C₂ =32/33 and this answer does not match the answer in my book.
Can somebody tell me what I’m doing wrong?