Question

Galina had two boxes with pieces of paper in each. In the first box, each piece of paper had one possible outcome from flipping a coin 4 times (e.g., HHTH). There was one piece of paper for every possible outcome. How many pieces of paper were in the first box?

a. Number of pieces in the first box: ________

b. Number of pieces in the second box: ________

Answer 1

a. Number of pieces in the first box: 16

b. Number of pieces in the second box: 16

Explanation:

In the first box, the possible outcomes from flipping a coin 4 times can be calculated using the formula for combinations. Each flip of the coin can result in either a head (H) or a tail (T), giving us 2 possibilities for each flip. With 4 coin flips, the total number of outcomes is 2 raised to the power of 4 (2^4), which equals 16. Therefore, there are 16 pieces of paper in the first box, each representing a unique sequence of heads and tails resulting from 4 coin flips.

As for the second box, assuming Galina placed all the outcomes from the first box into the second one, the count remains the same. Since each outcome from the first box is distinct and unique, transferring them to the second box does not alter their quantity. Thus, there are also 16 pieces of paper in the second box, mirroring the outcomes from the first box.

This concludes the explanation of the number of pieces in both boxes, which amounts to 16 pieces each, representing all the possible sequences resulting from flipping a coin 4 times.

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