If a bag contains 100 balls numbered from 1 to 100, what is the probability that a removed ball is odd or greater than 80?

To determine the probability that a removed ball is odd or greater than 80, we first analyze the two separate conditions and then combine them.

In the bag, there are 100 balls numbered from 1 to 100.

First, we consider the condition of selecting an odd-numbered ball. The odd numbers from 1 to 100 are: 1, 3, 5, ..., 99. This sequence has a total of 50 odd numbers (since every second number is odd in this range).

Next, we look at the second condition: selecting a ball with a number greater than 80. The numbers greater than 80 within the given set are 81, 82, 83, ..., 100. This condition also has 20 valid outcomes (80 through 100 inclusive).

Now, we need to find the overlap between the two conditions—the balls that are both odd and greater than 80, which would include: 81, 83, 85, ..., 99. This sequence also includes 10 numbers.

Applying the principle of inclusion-exclusion, the total count of favorable outcomes (which satisfy either condition) can be calculated as follows:

• Total odd balls: 50

• Total