Q:

Why we write probabilities int % and not out of 1

I always wondered why we write probabilities in % instead of out of 1 when out of 1 is more logical, for example if you are not familiar with percentages a 50% chance sounds like nothing but 1/2 sounds more logical since it says that is half possible. Also when you multiply probabilities one another you need to put them out of one. So why use percentage when out of one is more logical and practical?

A:

The short answer is: we're stuck with the convention due to historical habit.
Mathematicians understand that writing $50\%$ is just a particular way of expressing the probability $1/2$ - but that point of view is a relatively modern one. Probability didn't emerge as a field of study until a few centuries ago (around the Renaissance).
Expressing fractions of a whole as hundredths, on the other hand, dates back to Roman times (source):

In Ancient Rome, long before the existence of the decimal system, computations were often made in fractions which were multiples of 1⁄100. For example, Augustus levied a tax of 1⁄100 on goods sold at auction known as centesima rerum venalium. Computation with these fractions was similar to computing percentages. As denominations of money grew in the Middle Ages, computations with a denominator of 100 became more standard and from the late 15th century to the early 16th century it became common for arithmetic texts to include such computations. Many of these texts applied these methods to profit and loss, interest rates, and the Rule of Three. By the 17th century it was standard to quote interest rates in hundredths.

Thus, by the time mathematicians came to understand probabilities as fractions of a whole, there was already a millennia-old standard in place of using hundredths to express such a concept. Not the most elegant way of doing things, but the sciences are littered with examples of conventions that didn't turn out to be the most efficient. Plenty of engineers wish Ben Franklin had defined positive and negative charge the opposite way, for example. 
Also worth noting is that when mathematicians talk about probabilities, they usually do use fractions of $1$ rather than $100$ for reasons that include the ones you mention in your question. It's in areas where those concerns don't matter as much (such as saying there's a 40% chance of rain today) you're far more likely to see historical convention dominate because there's not as much value gained from being able to work with those numbers mathematically.

