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Forum URL:	http://www.cut-the-knot.org/cgi-bin/dcforum/forumctk.cgi
Forum Name:	High school
Topic ID:	149
#0, if you pick 3 numbers between 0 and 9 whats the probability that a dollar bill will have all 3 numbers in the ID number on the bill. the ID number has 8 numbers in it. I am looking for a formula not an answer - thanks Posted by nunzone on Apr-05-02 at 11:58 PM #1, pick 3 numbers Posted by jrr7 on May-09-02 at 02:57 PM In response to message #0 Let's call a "success" when all the numbers you picked show up on the bill, and a "failure" when not all of them are there. Do the three numbers you pick have to be different? Because to maximize my chances of success, I'd pick the same number all three times. That way I have eight opportunities for my guess to turn up. So I'll assume that the three numbers you pick have to be different. 10 choices for the first one, 9 left for the second one, 8 left for the third one. On any individual digit you have a 1-in-10 chance of making it, or a 9-in-10 chance of failure. If you only had to pick one number, your odds of failure would be (0.9)^8, about 43%. The probability of your number hitting all 8 is (0.1)^8, tiny. (There has to be a bill somewhere numbered 77777777 ) #2, 3 digits on a dollar bill's ID. Posted by browser on Jun-04-02 at 09:26 AM In response to message #0 Algorithm: 1.Find the probability of 3 successes out of 8 possibilities in the string. 2.Find the probability that the 3 successes are all different. 3.The product is the probability of 3 different digits appearing on the ID with all other digits different.