ping pong balls are numbered 1-20, with no repetition of any of the numbers. What is the probability of selecting one ball that is either odd or a number 4 ball? Select the correct answer below: 50% 5% 45% 55%
The Correct Answer and Explanation is:
Here is a detailed explanation of how to arrive at this answer.
This problem asks for the probability of a specific event when selecting a single ping pong ball from a set of 20. Probability is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes.
First, let’s identify the total number of possible outcomes. There are 20 ping pong balls, each numbered uniquely from 1 to 20. Therefore, when selecting one ball, there are 20 possible outcomes.
Next, we need to determine the number of favorable outcomes. The question asks for the probability of selecting a ball that is “either odd or a number 4 ball”. This means we need to count how many balls meet this condition. We can break this down into two parts:
- Count the odd-numbered balls: We need to find all the odd numbers between 1 and 20. These are: 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19. Counting these, we find there are 10 odd-numbered balls.
- Count the number 4 ball: There is only one ball with the number 4.
The event is selecting a ball that is odd OR the number 4. Since the number 4 is an even number, it is not included in our count of odd numbers. This means the two events, selecting an odd ball and selecting the number 4 ball, are mutually exclusive; they cannot happen at the same time. Therefore, to find the total number of favorable outcomes, we simply add the number of outcomes for each condition.
Total favorable outcomes = (Number of odd balls) + (Number of balls with the number 4)
Total favorable outcomes = 10 + 1 = 11
Now we can calculate the probability:
Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)
Probability = 11 / 20
To express this probability as a percentage, we multiply the fraction by 100:
Percentage = (11 / 20) * 100%
Percentage = 0.55 * 100%
Percentage = 55%
Thus, the probability of selecting one ball that is either odd or the number 4 is 55%.
