2015 AMC 10B Problems/Problem 11
Contents
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 1
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 (Listing)
Since the only primes digits are , , , and , it doesn't seem too hard to list all of the numbers out.
- 2- Prime;
- 3- Prime;
- 5- Prime;
- 7- Prime;
- 22- Composite;
- 23- Prime;
- 25- Composite;
- 27- Composite;
- 32- Composite;
- 33- Composite;
- 35- Composite;
- 37- Prime;
- 52- Composite;
- 53- Prime;
- 55- Composite;
- 57- Composite;
- 72- Composite;
- 73- Prime;
- 75- Composite;
- 77- Composite.
Counting it out, there are cases and of these are prime. So the answer is . ~JH. L
Video Solution 1
~Education, the Study of Everything
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.