Final answer:
The probability of getting exactly 3 heads when flipping a fair coin 8 times is calculated using the binomial coefficient, resulting in 56 valid combinations out of 256 possible outcomes, or 56/256. The correct answer is B. 56/256.
Step-by-step explanation:
When you flip a fair coin 8 times, and you want to calculate the probability of getting exactly 3 heads, you can use the concept of binomial probability. A binomial probability refers to the probability of exactly x successes in n trials, with the same probability of success on each trial.
In the case of the fair coin, the probability of getting a head on any given flip is 0.5. We can use the binomial coefficient, which is also known as 'n choose x' and is written as C(n, x). This gives us the number of combinations of n items taken x at a time and is calculated as C(n, x) = n! / (x! (n-x)!), where '!' denotes the factorial operation.
For n=8 flips and x=3 heads, the binomial coefficient C(8, 3) is equal to 8! / (3! * (8-3)!) giving us 56 combinations. The probability of each of these combinations occurring is (0.5)^3 for the heads and (0.5)^(8-3) for the tails. Therefore, the overall probability of getting exactly 3 heads in 8 flips is:
P(3 heads) = C(8, 3) * (0.5)^3 * (0.5)^(8-3)
P(3 heads) = 56 * (0.5)^3 * (0.5)^5
P(3 heads) = 56 / 256
Hence, the correct answer is B. 56/256.