1st USAMO 1972 Problem 3 n digits, none of them 0, are randomly (and independently) generated, find the probability that their product is divisible by 10. Solution
: 1 - (8/9) n - (5/9) n + (4/9) n . A number is divisible by 10 iff it has an even number and a 5 amongst its digits. The probability of no 5 is (8/9) n . The probability of no even number is (5/9) n . The probability of no 5 and no even number is (4/9) n . Hence result. 1st USAMO 1972 © John Scholes jscholes@kalva.demon.co.uk 13 Jul 2002 Last corrected/updated 20 Oct 03