The probability of a couple having either a boy or a girl is?. however, many families have more boys than girls and vice versa. why is the observed ratio of boys to girls in typical families different than the predicted ratio

Each birth is independent of the previous birth, if any. Just because a boy was born the first time doesn't mean the next birth will definitely be a boy. Most people, with the correct amount of chromosomal information, will definitely have one X chromosome, but the determinant for the gender of a child ultimately depends on the second chromosome - another X chromosome will yield a girl, while a Y chromosome will yield a boy.

Thus, it can be seen that there is a 50/50 chance at having a boy, and vice versa.

Like science, accuracy is dependent on the 'amount of tries' someone has overtime. This is why most scientists repeat experiments 10 000 times. For example, in order to generalise his case, Mendel had to repeat his experiment over 200 000 times with pea plants.

As we repeat the same event over a long period of time, we will begin to see a trend, and in this instance, the trend will terminate to approximately a 50/50 chance. However, most, if not all, families will not have repeated this event enough to warrant the estimated ratio, and thus, there are often differences in the estimated ratio.

The probability of having either a boy or a girl is statistically 0.5, and this makes sense at the chromosomal level - there are genetic reasons for it.

Why the observed ratio in families is different than predicted ratio is simply due to chance. Just like getting a string of heads when you flip a coin, you got 'lucky' - not real luck but just random coincidence. Your next coin toss could be a tail.