# Probability Properties

Next wewill see some properties that we often encounter when solving probability questions:

• When we have a probability composed of several possible outcomes the various probabilities must be summed to obtain the final probability.
• The sum total of the probabilities in any trial is $1$, i.e., the probability of a certain outcome plus the probability of not having a certain outcome is equal to $1$

## Let us demonstrate this with two examples

### Example 1

A die is rolled with $6$ faces numbered from $1$ to $6$.

The question is about the probability of an even number greater than $3$ when rolling a die.

Looking at the data we have, we see that the two numbers that fit these criteria are $4$ and $6$ because they are even and greater than $3$. The probability that $4$ will be rolled is $⅙$. The probability that $6$ will come up when rolling the die is also $\frac{1}{6}$

Having said this, we must add both probabilities as follows and obtain $\frac{1}{6}+\frac{1}{6}=\frac{2}{6}=\frac{1}{3}$

That is, the probability of rolling an even number greater than $3$ when rolling a die is $\frac{1}{3}$

### Example 2

The forecast has stated that the probability of snow tomorrow is $30%$.

From the above it follows that the probability of no snow tomorrow is $70%$.

We should see that the sum of the probabilities of the forecast with or without snow is $1$.

The probability of snow tomorrow is $\frac{30}{100}=\frac{3}{10}$
The probability of no snow tomorrow is $\frac{70}{100}=\frac{7}{10}$
From this it follows that the sum total of the probabilities is $\frac{3}{10}+\frac{7}{10}=\frac{10}{10}=1$