A jar contains only one blue tile, one green tile, one red tile, and one yellow tile. If a tile is chosen at random and then replaced in the jar, and then a second tile is chosen at random, how many of the possible outcomes contain at least one red tile?

There are 4 choices for each draw, so there are 4 × 4 = 16 ordered outcomes because the first tile is replaced. Count outcomes with no red tile: each draw then has 3 choices, giving 3 × 3 = 9. Thus, 16 − 9 = 7 outcomes contain at least one red tile, so the answer is 7.

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