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 digits that can be used in the code are 5, 6, 7, 8, and 9 .
That's five digits.

Two of them are prime numbers . . . 5 and 7 .

So the probability that the first digit is a prime number is

                           2 / 5  =  40% .

The code is an odd number if the last digit is an odd number.
Three of the possible digits are odd . . . 5, 7, and 9 .

So the probability that the last digit is odd . . . making the
whole code an odd number . . . is

                             3 / 5  = 60% .

By the way, the first digit can be any one of the 5 digits.
For each of those, the second one can be any one of the
remaining 4 digits.
For each of those, the third one can be any one of the
remaining 3 digits.

The total number of possible codes is  (5 x 4 x 3) = 60 codes.
40% of them (24 codes) start with a prime number.
60% of them (36 codes) are odd numbers.
Only 20% of them (12 codes) both start with a prime AND are odd numbers.