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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:

[tex]\[
\begin{array}{|l|c|c|c|c|}
\hline & \text{Red} & \text{Blue} & \text{White} & \text{Total} \\
\hline \text{Car} & 19 & 6 & 7 & 32 \\
\hline \text{Truck} & 8 & 16 & 9 & 33 \\
\hline \text{SUV} & 3 & 10 & 22 & 35 \\
\hline \text{Total} & 30 & 32 & 38 & 100 \\
\hline
\end{array}
\][/tex]

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]

Round your answer to the nearest whole percent.



Answer :

GinnyAnswer
To find the probability that a randomly selected vehicle is white given that it is an SUV, [tex]\( P(\text{White} \mid \text{SUV}) \)[/tex], we need to use the formula for conditional probability. This is expressed as:

[tex]\[ P(\text{White} \mid \text{SUV}) = \frac{P(\text{White and SUV})}{P(\text{SUV})} \][/tex]

From the two-way table provided, we can extract the following information:
- The total number of SUVs observed ([tex]\( P(\text{SUV}) \)[/tex]) is 35.
- The number of white SUVs ([tex]\( P(\text{White and SUV}) \)[/tex]) is 22.

Now, we compute the conditional probability:

[tex]\[ P(\text{White} \mid \text{SUV}) = \frac{22 \text{ white SUVs}}{35 \text{ total SUVs}} \][/tex]

To convert this fraction into a percentage, we perform the division and then multiply by 100:

[tex]\[ P(\text{White} \mid \text{SUV}) = \left(\frac{22}{35}\right) \times 100 \][/tex]

Performing the division:

[tex]\[ \frac{22}{35} \approx 0.6285714285714286 \][/tex]

Multiplying by 100 to convert to a percentage:

[tex]\[ 0.6285714285714286 \times 100 \approx 62.857142857142854 \][/tex]

Rounding to the nearest whole percent:

[tex]\[ P(\text{White} \mid \text{SUV}) \approx 63\% \][/tex]

Therefore, the probability that a randomly selected vehicle is white given that it is an SUV is approximately:

[tex]\[ \boxed{63\%} \][/tex]

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