Imagine someone producing a series of zeros and ones by reaching into the bag and placing them one by one on a game board. The probability of choosing a zero on the first pick is just 1 in 2. But the probability of choosing two consecutive zeros after placing the first back in the grab bag (and shaking the tiles) is 1 chance in 2 × 2, or 1 chance in 4. This is because there are four possible combinations of digits that could have been chosen—00, 01, 10, or 11. Similarly, the probability of producing any three-letter sequence as a result of choosing consecutively in this manner is 1 in 2 × 2 ×
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