Flip two coins 50 times and record the number of times exact

Flip two coins 50 times and record the number of times exactly one head was obtained. Determine the empirical probability of flipping exactly one head. How does this compare to the theoretical probability of flipping a coin and getting heads.

Solution

Expirical :
When I flipped 2 coins 50 times, i got exactly 1 head(HT or TH) a total of 23 times

And in the remaining 27 times, i got either TT or HH.

So, empirical probability of getting exactly one head was : 23/50 = 0.46 or 46%

Theoretical :
When we flip a single coin, we have two outcomes :

H
T

So, P(head) = 1 out of 2 = 1/2 = 0.5 or 50%

Comparison :

When i performed the experiment, got exactly 1 head 23 out of 50 times, which is 46%
Whereas, theoretically, I must have got exactly 1 head 25 out of 50 times, which is 50%

Probability is not an exact science. A person can flip 5 coins and get all 5 heads. This is a possible case albeit very very rare. What we expect in our experiment is that when the number of trials, i.e the number of coin flips is very very very very large, the probability of exactly 1 head will approach 50%. Our number of trials was 100, (2 coins flipped 50 times). In all likelihood, if we increase our number of trials to 1000 or 10000, the empirical probability that I obtained while performing the experiment will edge closer and closer to 50%