AMC10 2027 - Self-practice Set 1 Question 18

Question 18

Among the positive integers below $100$ whose every digit is prime, one is chosen uniformly at random. What is the probability that the selected number is prime?

$\frac8{99}$
$\frac25$
$\frac9{20}$
$\frac12$
$\frac9{16}$