# Problem #1962

 1962 Among the positive integers less than $100$, each of whose digits is a prime number, one is selected at random. What is the probablility that the selected number is prime? $\textbf{(A) } \dfrac{8}{99} \qquad\textbf{(B) } \dfrac{2}{5} \qquad\textbf{(C) } \dfrac{9}{20} \qquad\textbf{(D) } \dfrac{1}{2} \qquad\textbf{(E) } \dfrac{9}{16}$ This problem is copyrighted by the American Mathematics Competitions.
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• Reduce fractions to lowest terms and enter in the form 7/9.
• Numbers involving pi should be written as 7pi or 7pi/3 as appropriate.
• Square roots should be written as sqrt(3), 5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
• Exponents should be entered in the form 10^10.
• If the problem is multiple choice, enter the appropriate (capital) letter.
• Enter points with parentheses, like so: (4,5)
• Complex numbers should be entered in rectangular form unless otherwise specified, like so: 3+4i. If there is no real component, enter only the imaginary component (i.e. 2i, NOT 0+2i).