Given that a fair die is rolled. We know there are six numbers in a fair die.
On rolling a die, the Sample space of the given event E = {1, 2, 3, 4, 5, 6}
Sample space of numbers less than 5 = {1, 2, 3, 4}
Clearly we can see that the number of favorable outcomes = 4
Hence, P(values less than 5) = 4/6 = 2/3.
To find the complement of rolling a number less than 5, we use the formula P' = 1 - P, where P' is the complement of P.
So, let P' be the complement probability of getting numbers less than 5
Now, P'(numbers less than 5) = 1 - P(numbers less than 5)
= 1 - 2/3
= 1/3.
Hence, the probability of the complement of rolling a number less than 5 by using a six-sided die is 1/3.