n digits, none of them 0, are randomly (and independently) generated, find the probability that their product is divisible by 10.
Solution
Answer: 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.
© John Scholes
jscholes@kalva.demon.co.uk
13 Jul 2002
Last corrected/updated 20 Oct 03