Higher November 2023 Paper 3 Q16

16 Zia has to set a 4-digit security passcode on her phone.

Each digit of the passcode is a number from 1 to 9
She can use each number more than once.

Zia tells her friend Amber that
the first digit is a cube number
the second digit is a prime number
the third digit is greater than 6
the fourth digit is an odd number.

The diagram shows one possible 4-digit passcode.

Amber is going to have one attempt at guessing Zia’s passcode.

Work out the probability that Amber guesses Zia’s passcode on the first attempt. (3)