My first original question :P
Source of inspiration: Discussion with one of the seniors (CSE, IITB Alumnus 05-09 & Quant Analyst) during Pre-Placement Talk of a firm during Campus Placements - "I have seen your blog. Its very good. But its not original. Try and make your own questions."
Ever played housie/tambola? I played housie once every month for 6 good years of my life. Won some prizes. Each coupon (a ticket with 15 numbers) cost Rs. 10 then. Full Housie was nearly 150 Rs, exact number depending upon the number of tickets sold.
I played one such game once again after a lapse of 6 years I think. At the end of the game I saw that 76 numbers out of 90 had been cut on the board. I couldn't help but to think what is the expected number of numbers I expect to be crossed if N (say 100) tickets have been sold. Also, I wanted to find out what is a good number of people who should be there to play housie. Of course if there are zillions of people, the game would be over in approximately 15 calls. If there is one person, we expect the game to go on very close to 90 calls. What is the number of people playing the game so that the expected number of calls would be say 70.
Of course, I played the game in a homely environment where the "dealer" did not keep any money. So, all the money collected was given back as prizes. Since every person has equal expectation to win, I should expect to get back my investment.
The questions posed are:
1) What is the expected number of numbers I expect to be crossed if 100 tickets have been sold?
2) What is the number of people playing the game, i.e. the number of tickets sold so that the expected number of calls would be 70?
Cheers to my first original question :P
Solution: Analysis done by me and posted in comments!