Here is the discrete probability distribution for 50 coin flips where x = number of "heads" in 50 coin flips and P(x) is the probability that the outcome will be x coins turned up "heads".

Flipping a coin 50 times and counting the "heads" results in 51 distinct outcomes listed in the relative frequency table and the histogram.

As expected the most likely result is 25 heads and the farther away from 25 heads, the less likely the result.

Note that while it is possible that fewer than 14 heads, it is very unlikely, in fact on 0.05% likely. Similary, the probability that the number of heads is more than 36 is 0.05%.

With 99.99% probability, the number of heads will be 13 to 36!

This is the classic "bell-shape" of the so-called "normal" distribution.and centered at mean = 25 heads, as expected.

Use the empircal rule to confirm that this is indeed a very good approximation to a 'normal' distribution.