Question

Brian’s school locker has a three-digit combination lock that can be set using the numbers 5 to 9 (including 5 and 9), without repeating a number. The probability that the locker code begins with a prime number is %. The probability that the locker code is an odd number is %.

Answer 1

The possible digits are: 5, 6, 7, 8 and 9. Let's mark the case when the locker code begins with a prime number as A and the case when the locker code is an odd number as B. We have 5 different digits in total, 2 of which are prime (5 and 7).

First propability:
$P_A=\frac{2}{5}=40\%$

By knowing that digits don't repeat we can say that code is an odd number in case it ends with 5, 7 or 9 (three of five digits).

Second probability:
$P_B=\frac{3}{5}=60\%$