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Probability theory allows us to calculate the likelihood of multiple outcomes happening at the same time. In some situations, you are interested in knowing whether one event or another will occur. This is referred to as a **combined probability**.

A great way to determine the **combined probability** is to add together the probability of each individual event that is included. In our exercise, we know that 63% of voters are against the store moving in, and 17% are indifferent. To find the probability that a randomly selected voter is either against or indifferent, we take these two probabilities and sum them up:

• Probability of being against: 63%
• Probability of being indifferent: 17%
• Combined probability: 63% + 17% = 80%

By adding these probabilities, we find that there is an 80% chance a voter falls into one of these categories. It's important to ensure events are mutually exclusive in this context, meaning a voter cannot be both for and against at the same time.

In probability theory, expressing probabilities as decimals rather than percentages makes calculations simpler and more standard across different problems. A probability can be expressed as a decimal by dividing the percentage by 100.

Let's convert the 80% combined probability of being against or indifferent to a decimal:

• Start with 80%
• Convert percentage to decimal: \( \frac{80}{100} = 0.80 \)

This conversion helps streamline statistical calculations, making the numbers easier to work with without the potential confusion of percentages. Always remember that the probability as a decimal should always fall between 0 and 1, where 0 indicates an impossibility and 1 a certainty.

When calculating probabilities, the sum of all potential outcomes should equal 1, representing 100%. In this context of voters, not all are against the move or indifferent. Some do support the store’s move. This is why the combined probability of 0.80 is not equal to 1.

Here's the breakdown of probabilities:

• Voters against: 0.63
• Voters indifferent: 0.17
• Voters favoring: 0.20

Adding them together we get: \(0.63 + 0.17 + 0.20 = 1.00\). If you've accounted for every possibility, the probabilities should indeed sum up to 1.0, indicating a comprehensive look at all potential outcomes. This confirms that our calculated probabilities were correct, by including every section of the voter population.