Find the probability of obtaining between 50 and 55 tails inclusive when a fair coin is flipped 80 times. (answer accurate to four decimal places.)

To find the probability of obtaining between 50 and 55 tails (inclusive) when flipping a fair coin 80 times, you can use the binomial probability formula.

The binomial probability formula is given by:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Where:
- P(X = k) is the probability of getting k tails
- n is the total number of trials (in this case, 80 coin flips)
- k is the desired number of tails (between 50 and 55, inclusive)
- p is the probability of getting a tail on a single flip (0.5 for a fair coin)
- C(n, k) is the combination function, which calculates the number of ways to choose k tails from n flips. It can be calculated using the formula: C(n, k) = n! / (k! * (n-k)!)

Now let's calculate the probability.

First, let's calculate the probability of getting exactly 50 tails:
P(X = 50) = C(80, 50) * (0.5)^50 * (1-0.5)^(80-50)

Using the combination function, C(80, 50) = 80! / (50! * (80-50)!) = 3.1035366e+22

Therefore:
P(X = 50) = 3.1035366e+22 * (0.5)^50 * (0.5)^30

You will need a calculator or a programming language to calculate this value.
Substitute the values accordingly and calculate the probability.

Similarly, calculate the probability for 51, 52, 53, 54, and 55 tails using the same formula.

Finally, sum up the probabilities for getting between 50 and 55 tails (inclusive):
P(50 ≤ X ≤ 55) = P(X = 50) + P(X = 51) + P(X = 52) + P(X = 53) + P(X = 54) + P(X = 55)

This will give you the desired probability. Round the solution to four decimal places to provide the result.