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Empirical probability, also known as experimental probability, is measured based on the actual results of an experiment rather than theoretical expectations. It's the ratio of the number of times an event has occurred to the total number of trials or times that the activity has been performed.

For example, if you were to actually pull candies from the bag multiple times, keeping track of how many times you draw a red candy out of many attempts, you would be calculating the empirical probability. If out of 100 tries, you pulled out a red candy 28 times, the empirical probability for drawing a red candy would be \(\frac{28}{100} = 0.28\) or 28\%.

It's important to note that while empirical probability can give us an idea of likelihood from a practical standpoint, it may differ from theoretical probability due to the randomness and variability in short-term results. Over a large number of trials, however, the empirical probability tends to approach the theoretical probability.

Probability calculation is the process of determining the likelihood of an event occurring. To calculate theoretical probability, you would use a formula: \( P(E) = \frac{number \; of \; favorable \; outcomes}{total \; number \; of \; possible \; outcomes} \).

In the case of the candy bag, the favorable outcomes are the chances of pulling out a red candy, which is 3 (since there are 3 red candies). The total number of possible outcomes is the total number of candies, which is 10. Therefore, the theoretical probability calculation would be \(\frac{3}{10}\), resulting in a probability of 30%.

When calculating probability, it's crucial to be precise in identifying the total number of outcomes and the number of favorable outcomes to ensure the calculation reflects the actual probability of the event.

The probability ratio is essentially what you're finding when you calculate probability: it's a way to express the likelihood of an event as a fraction, decimal, or percentage. In the given example, the probability ratio of pulling a red candy from the bag is 3 to 10, because there are 3 red candies and 10 candies in total.

A probability ratio is often simplified or converted into a decimal or percentage to be more intuitive. So, a 3 to 10 ratio is the same as saying '30 out of 100 times' (\(0.3\) in decimal, or 30% in percentage), which makes it clear that there's a 30% chance of drawing a red candy in any single attempt.

It's also worth noting that the sum of the probability ratios for all possible outcomes in a situation will always equal 1 (or 100%). This is because one of the possible outcomes must occur when an event happens, covering the entire range of possibilities.