Problem:
Among the positive integers less than , each of whose digits is a prime number, one is selected at random. What is the probability that the selected number is prime?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are four one-digit primes (, and ), which can be used to form two-digit numbers with prime digits. Of these two-digit numbers, only , and are prime. So there are numbers less than whose digits are prime, and of them are prime. The probability is .
The problems on this page are the property of the MAA's American Mathematics Competitions