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A student observed the color and type of vehicle that passed by his school for an hour. The two-way table is given below:

\begin{tabular}{|l|c|c|c|c|}
\hline & Red & Blue & White & Total \\
\hline Car & 19 & 6 & 7 & 32 \\
\hline Truck & 8 & 16 & 9 & 33 \\
\hline SUV & 3 & 10 & 22 & 35 \\
\hline \multicolumn{1}{|c|}{ Total } & 30 & 32 & 38 & 100 \\
\hline
\end{tabular}

What is the probability that a randomly selected vehicle from this observation is white, given that it's an SUV?
[tex]\[ P(\text{White} \mid \text{SUV}) = [?] \% \][/tex]



Answer :

GinnyAnswer
To determine the probability that a randomly selected SUV is white, we follow these steps:

1. Identify the total number of SUVs observed:
- From the table, we see that the total number of SUVs is 35.

2. Identify the number of white SUVs observed:
- From the table, the number of white SUVs is 22.

3. Calculate the probability [tex]\(P(\text{White} \mid \text{SUV})\)[/tex]:
- This probability is the number of white SUVs divided by the total number of SUVs, expressed as a percentage.

4. Performing the division and converting to a percentage:
- [tex]\(P(\text{White} \mid \text{SUV}) = \frac{22}{35} \times 100\)[/tex]

5. Upon calculation, the probability that a randomly selected SUV is white is approximately 62.8571%.

So, the probability that a randomly selected vehicle is white given that it's an SUV is [tex]\( \boxed{62.8571\%} \)[/tex].

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