emon wrote:
Michel is drawing 2 winning tickets from a bucket of raffle tickets she sold. She sold atleast 14 but not more than 22 tickets. If James bought two tickets from Michel and tickets are not returned to the drawing bucket after they have been drawn what is the lowest possible probability that he will win both prizes?
The OA is not given.
Can somebody please help me with this one. It will be very helpful if you explain every step.
Thanks.
Hi Emon, I'll try and walk you through this. Please let me know if anything is unclear or if I maybe misunderstood something.
If James has the two winning tickets, and the question is asking the lowest possible probability that he won both prizes, then we need to maximize the number of tickets sold (i.e. 22). If they only sold 2 tickets, he'd be a guaranteed winner, so the more tickets sold, the less chance he has to be the winner.
Now that we know there are 22 tickets sold, and James has 2, what are the chances that the first one will be a winner? His number of tickets over the total number of tickets, so 2/22. We only care about the scenario where he wins, so let's assume he wins the first drawing. For the second drawing, he now has 1 chance out of 21 remaining tickets to win, so 1/21. Multiplying these two together (and simplifying by 2) we get
1/11 * 1/21 = 1/232. He has about a half a percentage chance to win both drawings if she sold 22 tickets.
Again, if she'd sold 20, 18 or 14 tickets, James' odds of winning would go up, so the lowest percentage possible should be 1/232, i.e. the odds that he wins the first x the odds that he wins the second.
Hope this helps!
-Ron