Sure, let's define the variables in the binomial probability formula related to the given statement:
1. Total Number of Trials (n):
The number of trials represents the total number of coin flips. In this case, we are flipping a coin 10 times.
[tex]\[
n = 10
\][/tex]
2. Probability of Success on a Single Trial (p):
The probability of success in this context is the probability of flipping a "head" on a single trial. Given a fair coin, the probability of getting heads is 0.5.
[tex]\[
p = 0.5
\][/tex]
3. Number of Successes (k):
The number of successes represents the specific number of "heads" we are interested in. Here, we are interested in getting exactly 5 heads out of the 10 flips.
[tex]\[
k = 5
\][/tex]
4. Binomial Probability (P):
We are interested in the probability of getting exactly 5 heads (successes) out of 10 coin flips (trials) with the probability of a single trial being heads at 0.5. This probability can be evaluated using a binomial distribution function.
The result given is:
[tex]\[
\text{Binomial Probability} = 0.24609375000000003
\][/tex]
So to summarize:
[tex]\[
n = 10, \quad p = 0.5, \quad k = 5, \quad \text{Probability} = 0.24609375000000003
\][/tex]
This means the probability of getting exactly 5 heads in 10 coin flips is 0.24609375000000003.
