Here is the explanation in a simple format:

### Definition of a Binomial Distribution:
A binomial distribution is a probability distribution that represents the number of successes in a fixed number of trials. Each trial has two possible outcomes: success or failure. The probability of success is the same in each trial.

The formula for the probability of exactly **k** successes in **n** trials is:
P(X = k) = (n choose k) * p^k * (1 – p)^(n – k)

Where:
– n = number of trials
– p = probability of success
– k = number of successes

### Problem:
What is the probability of obtaining exactly 2 heads in 5 flips of a fair coin?

For a fair coin:
– n = 5 (flipping the coin 5 times)
– p = 0.5 (probability of getting heads)
– k = 2 (we want exactly 2 heads)

Using the binomial formula:
P(X = 2) = (5 choose 2) * (0.5)^2 * (0.5)^3

First, calculate the binomial coefficient (5 choose 2):
(5 choose 2) = 5! / (2!(5 – 2)!) = 10

Now, calculate the probability:
P(X = 2) = 10 * (0.5)^2 * (0.5)^3 = 10 * 0.25 * 0.125 = 0.3125

The probability of obtaining exactly 2 heads in 5 flips of a fair coin is 0.3125 or 31.25%.