MATH SOLVE

3 months ago

Q:
# If a fair coin is flipped 50 times, what is the probability of 25 heads?

Accepted Solution

A:

The correct answer is 0.11.

Explanation:

This is binomial, as there are a fixed number of trials, the probability of each trial is independent, and there are only two outcomes. Since that is the case, we will calculate:

[tex]_nC_r(p)^r(1-p)^{n-r}=_{50}C_{25}(0.5)^{25}(1-0.5)^{50-25} \\ \\=\frac{50!}{25!25!}(0.5^{25})(0.5^{25})=0.11[/tex]

Explanation:

This is binomial, as there are a fixed number of trials, the probability of each trial is independent, and there are only two outcomes. Since that is the case, we will calculate:

[tex]_nC_r(p)^r(1-p)^{n-r}=_{50}C_{25}(0.5)^{25}(1-0.5)^{50-25} \\ \\=\frac{50!}{25!25!}(0.5^{25})(0.5^{25})=0.11[/tex]