how many possible outcomes exist when four fair coins are flipped?\n2\n4\n8\n16

Explanation:

Step1: Analyze one - coin flip

Each fair coin has 2 possible outcomes (heads or tails), i.e., $n_1 = 2$.

Step2: Use the multiplication principle for multiple - coin flips

When 4 coins are flipped, and since the flips are independent events, the total number of possible outcomes $N$ is given by the product of the number of outcomes for each coin flip. Using the formula $N=n_1\times n_2\times n_3\times n_4$. Since $n_1 = n_2=n_3=n_4 = 2$, we have $N = 2\times2\times2\times2=2^4$.

Step3: Calculate the result

$2^4=16$.

Answer:

16