To understand the probability of the complement of rolling a number less than 5 on a six-sided die, we first determine what constitutes rolling a number less than 5. The numbers on a standard die are 1, 2, 3, 4, 5, and 6. Therefore, the numbers less than 5 are 1, 2, 3, and 4. This gives us 4 favorable outcomes.
The total number of possible outcomes when rolling a six-sided die is 6. Hence, the probability of rolling a number less than 5 can be calculated as:
P(rolling less than 5) = Favorable outcomes / Total outcomes
P(rolling less than 5) = 4 / 6 = 2 / 3
Now, the complement of an event is defined as the event that the favorable outcome does not happen. So, the complement of rolling a number less than 5 means rolling a number that is 5 or 6.
There are 2 outcomes (5 and 6) that make up this complement. Therefore, the probability of the complement can be calculated as:
P(complement of rolling less than 5) = Favorable outcomes of the complement / Total outcomes
P(complement of rolling less than 5) = 2 / 6 = 1 / 3
In conclusion, the probability of the complement of rolling a number less than 5 on a six-sided die is 1/3.