SAT Question 9ce8cbbe: Probability And Conditional Probability answer and explanation with Desmos solution

Choice A is correct. It's given that set K consists of all the positive integers that are less than or equal to $160$, where none of the integers are repeated. Therefore, set K consists of the integers $1$ through $160$, which is $160$ numbers. Of these, the integers $1$ through $50$ are less than or equal to $50$. Therefore, there are $50$ numbers that belong to set K that are less than or equal to $50$. Of these, half are even. Therefore, $\frac{50}{2}$, or $25$, numbers that belong to set K are even and less than or equal to $50$. The probability of selecting at random a number from set K that is even and less than or equal to $50$ is equal to the number of numbers that belong to set K that are even and less than or equal to $50$, which is $25$, divided by the total number of numbers that belong to set K, which is $160$. It follows that the probability of selecting at random from set K a number that is even and less than or equal to $50$ is $\frac{25}{160}$, or $\frac{5}{32}$.