# What is the probability of the complement of rolling a number less than 5 by using a six-sided die?

**Solution:**

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.

## What is the probability of the complement of rolling a number less than 5 by using a six-sided die?

**Summary**:

The probability of the complement of rolling a number less than 5 by using a six-sided die is 1/3.

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