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When dealing with probability, one of the fundamental concepts is identifying the *favorable outcomes*. This refers to the specific outcomes that meet the conditions of the event we're interested in. For instance, in our given exercise, we want to know the probability of drawing a ball that is neither yellow nor red from the jar.

To find this, we first focus on counting only the outcomes that fit this requirement. In this case, the jar has:

• 10 black balls
• 14 green balls

Any draw of a black or green ball is considered a favorable outcome.

It's important to be precise when specifying what constitutes a favorable outcome. Misidentifying these can lead to incorrect calculations. Remember, favorable outcomes are those that directly satisfy the event's conditions.

Next, let's understand the concept of *total outcomes*. In probability, total outcomes refer to all possible outcomes of an experiment. For any probability question, we need to know the total number of outcomes in the sample space, which is the set of all possible results.

In our exercise, the sample space consists of all balls in the jar. We need to count them all to find the total number of outcomes:

• 10 black balls
• 23 yellow balls
• 14 green balls
• 3 red balls

Adding these together gives us the total number of balls: 10 + 23 + 14 + 3 = 50. So, there are 50 possible outcomes when drawing any ball from the jar.

Knowing the total number of outcomes is crucial because it forms the denominator in the probability fraction.

The final step is to calculate the *event probability*. This involves finding the ratio of favorable outcomes to the total number of outcomes. The formula for probability is: \[ \text{Probability} = \frac{ \text{Favorable outcomes} }{ \text{Total outcomes} } \]

In our exercise, the favorable outcomes are the black and green balls, total of 24 balls. The total outcomes, as we calculated, are 50. So the probability is:
\(\frac{24}{50}\)

Simplifying this fraction, we get: \[ \frac{24}{50} = \frac{12}{25} \]

Therefore, the probability of drawing a ball that is neither yellow nor red is \(\frac{12}{25}\).

Always double-check each part: favorable outcomes, total outcomes, and the calculation steps to ensure accuracy. Understanding these core concepts will make solving probability problems much easier!