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In probability, we often start with percentages that express how likely an event is.
To convert these percentages into probabilities, we simply divide them by 100.
This places the percentage into a decimal form, suitable for probability calculations.

For example, if you know that 9.6% of people traveled by car, you convert this to a probability by calculating \( \frac{9.6}{100} = 0.096 \).
Similarly, for those who stayed home which is given as 88.09%, the probability would be \( \frac{88.09}{100} = 0.8809 \).

These conversions are essential because probabilities in mathematics are always between 0 and 1.
0 means an event will not happen, and 1 means it will definitely happen.
Therefore, percentages allow for a clear bridge to understanding and utilizing these concepts in practical problem-solving.

In situations where you need to find the probability of one event happening or another, it's about combining probabilities.
This is often referred to as finding the "union" of two events.
For example, what's the chance of "either traveling by car or staying home"? We find this by adding the individual probabilities.

In our scenario, we calculated:

• The probability of traveling by car: 0.096
• The probability of staying at home: 0.8809

Add them together, 0.096 + 0.8809, to get a combined probability of 0.9769.
This calculation represents the likelihood of one event or the other happening, known as their union.
It's useful for understanding how often one of several different outcomes might occur.

Understanding the union of events is key in probability.
When you ask about the union, you're essentially asking what the chance is that at least one of several events will happen.
This is crucial when considering multiple possibilities.

In terms of our example, calculating the union of staying home or traveling by car was straightforward.
However, the total probability of all possible events must equal 1.
In our solution, it didn't, because we didn't account for other modes of travel, like air or train.
This leftover percentage accounts for the rest of the possibilities we didn't include.

Realizing this helps us understand how to include all outcomes and recognize gaps in our initial assumptions.
The union of all possible events indeed sums up to 1, ensuring a complete evaluation of the situation.