Probability Properties

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 $\frac{1}{3}$

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 $1$.

Let us return to our data.

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 $\frac{3}{10}+\frac{7}{10}=\frac{10}{10}=1$