How does this binomial distribution look? Let’s take the example of tossing a coin. If we toss it 5 times we want to know the probability it will never land heads (0 times), the probability it will land heads 1 time, etc. The distribution is plotted below:

The distribution peaks at 2 and 3. So it’s most likely you’ll see two heads or 3 heads (i.e. two tails). Now lets go from 5 to 10 tosses:

Now the distribution looks a bit sharper, and it’s most likely to get 5 heads.

Now lets go to a total of 50 tosses:

Now you see it’s most likely to end up with 25 heads, but still quite likely to get 20. However it’s really unlikely to be less than 10 heads or more than 40 heads. The distribution has become much more like a brontosaurus, small at both ends and big in the middle.