There are 4 possible first draws.
The probability that your first draw is a $100 note is 3/4 since 3/4 notes are $100 notes.
If you can change boxes, there’s a 2/3 chance of drawing another $100 note. 2 of the 3 remaining notes are $100, thus, your chance of starting another $100 is 2/3.
If you aren’t allowed to change boxes, that second note is either a $1 or $100 note. The chance that it’s a $100 note is 1/2. However, since you can’t change your box, and you had a probability of 1/2 of choosing the box with two $100 notes, the probability is 1/2.
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