Originally Posted by

**SpringFan25** you can do this with a tree diagram, where each branch has 2 possible outcome (correct, not correct).

I wouldn't try and draw the whole thing, but its good to ahve in the back of your head.

**Step 1:**

Find the probability that no paycheck is in the correct envelope:

P(0) = $\displaystyle \frac{n-1}{n} \times \frac{n-2}{n-3} \times .... \frac{1}{2}$

$\displaystyle = \frac{(n-1)(n-2)....2}{n (n-1) (n-2)....2 \times 1}$

$\displaystyle =\frac{1}{n}$

**Step 2:**

P(at least 1) = 1-P(0)

$\displaystyle =\frac{n-1}{n}$

Check for n=3:

$\displaystyle \frac{3-1}{3} = \frac{2}{3}$, which you said was correct