To determine the probability that a customer has purchased an SUV or a blue car, let's go through the calculations step-by-step:
1. Calculate the total number of cars sold:
We sum up all the cars regardless of color or type.
[tex]\[
\text{Total number of cars} = 17 + 17 + 43 + 7 + 19 + 37 + 3 + 23 + 53 = 219
\][/tex]
2. Calculate the total number of blue cars:
We add up the number of blue cars for each type.
[tex]\[
\text{Total number of blue cars} = 17\ (\text{Sedan}) + 19\ (\text{SUV}) + 23\ (\text{Truck}) = 59
\][/tex]
3. Calculate the total number of SUVs:
We add up all the cars that are SUVs, regardless of color.
[tex]\[
\text{Total number of SUVs} = 7\ (\text{Red}) + 19\ (\text{Blue}) + 37\ (\text{White}) = 63
\][/tex]
4. Calculate the number of blue SUVs:
Specifically identify the blue SUVs.
[tex]\[
\text{Number of blue SUVs} = 19
\][/tex]
5. Calculate the probability of a customer having purchased an SUV or a blue car:
We use the formula for the probability of the union of two events:
[tex]\[
P(\text{Blue or SUV}) = P(\text{Blue}) + P(\text{SUV}) - P(\text{Blue and SUV})
\][/tex]
Substituting the numbers, we get:
[tex]\[
P(\text{Blue or SUV}) = \frac{59}{219} + \frac{63}{219} - \frac{19}{219}
\][/tex]
Combining the fractions:
[tex]\[
P(\text{Blue or SUV}) = \frac{59 + 63 - 19}{219} = \frac{103}{219}
\][/tex]
This fraction simplifies to:
[tex]\[
P(\text{Blue or SUV}) \approx 0.4703196347031963
\][/tex]
Thus, the probability that a randomly chosen customer purchased an SUV or a blue car is approximately [tex]\(0.4703\)[/tex].
