2015 AMC 10B Problems/Problem 11
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?
Solution
The one digit prime numbers are ,
,
, and
. So there are a total of
ways to choose a two digit number with both digits as primes and
ways to choose a one digit prime, for a total of
ways. Out of these
,
,
,
,
,
,
, and
are prime. Thus the probability is
.
Solution 2
We count the number of primes. We get 25 primes. The only answer choice that has a denominator of 25 (or simplified) is B.
Video Solution
~savannahsolver
See Also
2015 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.