Question

Galina had two boxes with pieces of paper each. In each 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) 8

B) 16

C) 24

D) 32

Answer 1

Galina's first box would contain 16 pieces of paper, as there are 16 possible outcomes from flipping a coin 4 times, with each flip doubling the number of outcomes.

Step-by-step explanation:

To determine how many pieces of paper were in the first box with all possible outcomes from flipping a coin 4 times, we must calculate the total number of outcomes. When flipping a coin once, there are two possible outcomes: heads (H) or tails (T). For each flip of the coin, the number of outcomes doubles since each outcome can lead to either an H or T on the next flip.

For one flip: 2 outcomes (H, T)

For two flips: 2 × 2 = 4 outcomes (HH, HT, TH, TT)

For three flips: 2 × 2 × 2 = 8 outcomes

For four flips: 2 × 2 × 2 × 2 = 16 outcomes

Therefore, the first box would contain 16 pieces of paper, with each piece representing one of the possible outcomes from flipping a coin 4 times.