*This is a real world problem we're trying to solve, not a test question, so in a way, your help is all the more appreciated!*
A student taking a test is presented with a question with five options. Among the 5 options presented, 2 of the 5 represent correct answers. (So, for example, if A, B, C, D and E are the options, it may be that B and E are correct.)

They may choose

*up to* 2 options; they can opt to select only 1 option, but may select 2. They may not select more than 2. (Essentially, think of 5 check boxes: they may not select more than 2, but they do have the option of selecting only 1.)

We know that the probability of selecting

**both** options correct (i.e., marking two check boxes, and both selections are correct) is represented by the following:

Here's what we need help with.

**Please remember that they do have the option of only marking 1 out of the 5 check boxes.** - What is the probability that they will get
**only 1** option correct (that either (a) they mark only 1 check box, and it is a correct one, or (b) they mark 2 check boxes, and 1 is right, but 1 is wrong)? - What is the probability that they will get
**at least 1** option correct (that either (a) they mark only 1 check box, and it is a correct one, (b) they mark 2 check boxes, and 1 of the 2 is correct, or also (c) they mark 2 check boxes, and both are correct)?

Essentially, we need to know the different probabilities for getting

**only 1** correct, versus getting

**at least 1** correct ... and we don't know how to account for their option to only mark 1 checkbox, not two.