In order to solve this problem, we need to discuss probabilities. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:

$\displaystyle P=\frac{\textup{event: particular phenomenon we wish to observe}}{\textup{sample space: total number of possible outcomes}}$

Let's use a simple example: the rolling of a die. We want to know the probability of rolling a one. We know that the sample space is six because there are six sides or outcomes to the die. Also, we know that there is only a single side with a value of one; therefore,

$\displaystyle P=\frac{1}{6}$

Now, let's convert this into a percentage:

$\displaystyle \frac{1}{6}=0.1666$

$\displaystyle 0.1666\times100\%=16.66\%$

Probabilities expressed in fraction form will have values between zero and one. One indicates that an event will definitely occur, while zero indicates that an event will not occur. Likewise, probabilities expressed as percentages possess values between zero and one hundred percent where probabilities closer to zero are unlikely to occur and those close to one hundred percent are more likely to occur. 

$\displaystyle 0< P< 1 \textup{ or }0\%< P< 100\%$

Now, we can discuss other terms related with probabilities. The complement of an event is the outcomes that do not include the event. In other words, what is the probability of not rolling one? For instance, in the previous example, we wanted to know the probability of rolling a one on a die. The complement of this event would be rolling everything but a one. The event in the complement would be rolling a two, three, four, five, or a six. We can calculate the probability using the following method:

$\displaystyle P=\frac{5}{6}$

Convert to a percentage.

$\displaystyle \frac{5}{6}=0.8333$

$\displaystyle 0.8333\times100\%=83.33\%$

We can also find the complement by subtracting the probability of the event from the maximum probability value of one:

$\displaystyle P_c_o_m_p_l_e_m_e_n_t=1-P$

It is important to note that in this case the complement is more likely to occur than the original event. 

Next, lets discuss unions and intersections. Regarding probabilities, a union is the likelihood that one event or another will occur. For instance, what is the probability that a person will role a one or a six on a die? 

$\displaystyle P=\frac{1+1}{6}=\frac{1}{3}$

Convert to a percentage.

$\displaystyle \frac{1}{3}=0.3333$

$\displaystyle 0.3333\times100\%=33.33\%$

Last, an intersection is the likelihood that one event will occur with another. What is the probability that we will roll a one and flip a coin to reveal "heads"? We know that the probability of rolling a one is:

$\displaystyle P=\frac{1}{6}$

Now, let's determine the probability of flipping a coin to reveal the "heads" side. A coin has two sides: heads or tails. The probability of rolling heads is as follows:

$\displaystyle P=\frac{1}{2}$

An intersection is the probability of two events occurring simultaneously; therefore, we need to multiply the probabilities.

$\displaystyle P=\frac{1}{12}$

Convert to a percentage.

$\displaystyle \frac{1}{12}=0.0833$

$\displaystyle 0.0833\times100\%=8.33\%$

Let's look at a table that contains these specific probabilities and the key words that are indicative of each. 

Now, let's use this question to solve the problem. The question asks us to find the probability of an intersection: cars that are royal blue with V8 engines. 

$\displaystyle P=\frac{\textup{event}}{\textup{sample space}}$

$\displaystyle P=\frac{92}{500}$

Convert to a percentage.

$\displaystyle \frac{92}{500}=0.184$

$\displaystyle 0.184\times100\%=18.4\%$