SAT Question 89ff6a0a: Probability And Conditional Probability answer and explanation with Desmos solution

It’s given that one button will be selected at random out of a total of $100$ buttons and that the table shows the distribution of buttons by group and diameter. The probability of selecting a button with a diameter less than or equal to $30$ millimeters, given that it is not in group 2, is the number of buttons with a diameter less than or equal to $30$ millimeters that are not in group 2 divided by the total number of buttons not in group 2. Based on the table, the buttons not in group 2 are those in group 1 and group 3. In group 1, there are $12$ buttons with a diameter less than $20$ millimeters and $8$ buttons with a diameter from $20$ to $30$ millimeters, which yields $12+8$, or $20$, buttons with a diameter less than or equal to $30$ millimeters. In group 3, there are $10$ buttons with a diameter less than $20$ millimeters and $32$ buttons with a diameter from $20$ to $30$ millimeters, which yields $10+32$, or $42$, buttons with a diameter less than or equal to $30$ millimeters. Therefore, the total number of buttons with a diameter less than or equal to $30$ millimeters that are not in group 2 is $20+42$, or $62$. The total number of buttons that are not in group 2 is the sum of all buttons in group 1 and group 3. There are $12+8+3$, or $23$, buttons in group 1 and $10+32+0$, or $42$, buttons in group 3. Therefore, the total number of buttons in groups 1 and 3 is $23+42$, or $65$. It follows that the probability of selecting a button with a diameter less than or equal to $30$ millimeters, given that it is not in group 2, is $\frac{62}{65}$. Note that .9538 and 62/65 are examples of ways to enter a correct answer.