To determine the probability of randomly selecting a certain type of integer from all positive two-digit integers, we first need to establish our sample space and the conditions that define the integers we’re interested in.
The range of positive two-digit integers is from 10 to 99, inclusive. This gives us a total of:
99 – 10 + 1 = 90 two-digit integers.
Next, we specify the property we are checking against. For example, if we want to find the probability that a randomly selected two-digit integer is even, we would count how many of these integers fit that criterion.
There are 45 even integers within the range of two-digit numbers (10, 12, 14, …, 98). The probability of selecting an even integer can thus be calculated using the formula for probability:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Hence, the probability of selecting an even integer would be:
Probability = 45 / 90 = 1/2
In general, you would follow this method for any property you wish to analyze by counting all integers that satisfy the condition and then dividing by the total number of two-digit integers, which is always 90.