To determine the probability that a randomly selected positive two-digit integer exhibits specific characteristics, we first need to identify the total range of positive two-digit integers.
The two-digit integers range from 10 to 99. This gives us:
- Lowest two-digit integer: 10
- Highest two-digit integer: 99
Now, let’s calculate the total count of two-digit integers:
Total two-digit integers = Highest – Lowest + 1 = 99 – 10 + 1 = 90.
Next, we should specify what characteristic or characteristics you are interested in examining (e.g., being even, being a prime number, having a particular digit, etc.). For instance, if we consider:
- Even integers: The even two-digit integers within this range are 10, 12, 14, …, 98. The first even number is 10, and the last is 98. To find the count of even numbers, we can use an arithmetic sequence formula:
Even integers = First + (n – 1) * Common difference, where n is the number of terms. Here, the common difference is 2:
- Count of even integers = (98 – 10) / 2 + 1 = 45.
So, if we consider the probability of selecting an even integer:
Probability (even) = Number of even integers / Total two-digit integers = 45 / 90 = 0.5 or 50%.
As you can see, the probability will vary based on the characteristics you want to examine. If you are looking for something else, feel free to specify!
In summary, the probability of a randomly chosen positive two-digit integer having a specific property is calculated by dividing the count of integers with that property by the total 90 two-digit integers.