Probability Question- CFA Level 1

Florence Hixon is screening a set of 100 stocks based on two criteria (Criterion 1 and Criterion 2). She set the passing level such that 50% of the stocks passed each screen. For these stocks, the values for Criterion 1 and Criterion 2 are not independent but are positively related. How many stocks should pass Hixon’s two screens?

Less than, more than or equal to 25?

What do you think?

Why?

I think that it should be less since the they are positively related more of the same stocks will pass both screens. Since they aren’t independent, 25 is not the answer but since it is the same stocks, it should be less than 25.

Let’s take an extreme example: Criterion 1 and Criterion 2 are identical. Clearly, they’re not independent, and they’re positively related. How many stocks should pass both screens?