Question

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

Answer 1

Answer: Probability of getting 25 heads is 0.11 or 11%.

Step-by-step explanation:

Since we have given that

A fair coin is tossed 50 times.

So, here, N = 50

Probability of getting a head = $\dfrac{1}{2}$

Probability of getting a tail = $\dfrac{1}{2}$

So, we will apply "Binomial distribution":

Let X is the number of getting heads.

$P(X=25)=^{50}C_{25}p^{25}q^{25}$

Here, $p=0.5,\ q=0.5$

So, it becomes,

$P(X=25)=^{50}C_{25}(0.5)^{25}\times (0.5)^{25}\\\\P(X=25)=0.1122\\\\P(X=25)\approx 0.11$

Hence, Probability of getting 25 heads is 0.11 or 11%.

Answer 2

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:
$_nC_r(p)^r(1-p)^{n-r}=_{50}C_{25}(0.5)^{25}(1-0.5)^{50-25} \\ \\=\frac{50!}{25!25!}(0.5^{25})(0.5^{25})=0.11$