Question

22
Liam is trying to remember a 3-digit code.
He knows the rule that
the first digit is a cube number
the second digit is a factor of 16
the third digit is an odd number.
Liam tries at random a code that matches the rule.
Work out the probability that this is the correct code.
[4 marks]

Answer 1

The first digit may be 1 or 8.

The second digit may be 1, 2, 4, 8.

The third digit may be 1, 3, 5, 7, 9.

There are $2\times4\times5=40\:variants$

The probability that this is the correct code is $\frac{1}{40}$