About This Set

Most questions here take two steps: two balls or two cards drawn together (count the pairs with nC2=n(n−1)2^{n}C_{2} = \frac{n(n-1)}{2}), an overlap to take off, a complement, or two people's chances put together. Three mistakes come up again and again at this level: a draw without replacement worked as if the first ball went back, exactly one of two people counted in only one way, and the chances of a race, where only one can win, multiplied when they should be added. Give it 25 minutes; with 19 or more right, move on to Practice Set 3.