Question

a fair coin is flipped 10 times. what is the probability of getting the same number of heads and tails

Answer 1

If you flip a coin one time, the probability to get a Head is

p = 1/2

The probability of not getting a head in a single toss is :

q = 1 - 1/2 = 1/2

Thus there is only one unique situation to get the same number of heads and tails : in 10 toss you need to get exactly five heads, it will means that the rest is the tails.

Now using Binomial theorem of probability, the probability of getting exactly x = 5 heads in a total of n = 10 tosses is :

P(X = 5) = $\frac{10!}{5!*5!} *(\frac{1}{2})^{5} *(\frac{1}{2})^{5}$≈ 0.246

So the probability of that is 24,6 %

Good Luck