The exact probability of getting a number greater than 25, when selecting from numbers 1 to 50, is 0.5 (or 1/2).
Understanding the Probability
To calculate the probability, we need to determine two key values: the total number of possible outcomes and the number of favorable outcomes (outcomes that meet our condition).
Defining the Sample Space
In this scenario, the context implies a set of numbers ranging from 1 to 50. This means:
- Total Outcomes: There are 50 distinct numbers from 1 to 50.
Identifying Favorable Outcomes
We are looking for numbers that are greater than 25. These numbers start from 26 and go up to 50.
- Numbers greater than 25: 26, 27, 28, ..., 50.
- To count these, we can subtract the starting point from the end point and add one (inclusive count): 50 - 26 + 1 = 25 numbers.
- Alternatively, using the reference's logic, if there are 50 total numbers and we want numbers greater than 25, it means we exclude 1 through 25. So, 50 - 25 = 25 numbers remain that are greater than 25.
- Favorable Outcomes: There are 25 numbers greater than 25.
Calculating the Probability
Probability is calculated using the formula:
$$ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} $$
Let's put our values into the formula:
- Number of Favorable Outcomes = 25
- Total Number of Outcomes = 50
$$ \text{Probability} = \frac{25}{50} = \frac{1}{2} = 0.5 $$
Summary of Probability Calculation
| Factor | Value | Explanation |
|---|---|---|
| Total Outcomes | 50 | All possible numbers from 1 to 50. |
| Favorable Outcomes | 25 | Numbers greater than 25 (i.e., 26 through 50). |
| Probability | 0.5 | Calculated as Favorable Outcomes / Total Outcomes. |
Practical Insight
A probability of 0.5 means there is a 50% chance of getting a number greater than 25. This indicates an equal likelihood of the event occurring or not occurring. For every two numbers you might randomly pick from 1 to 50, on average, one would be greater than 25.
