The following table gives information on the type of vehicle driven by gender fo
ID: 3172608 • Letter: T
Question
The following table gives information on the type of vehicle driven by gender for 200 randomly selected vehicles observed in Summit County.
Car
SUV
Truck
Male
20
45
30
Female
60
35
10
If one vehicle is selected at random, find the probability that:
a) The driver is a male, given that the vehicle is a car. _______
b) The vehicle is a truck driven by a female. _______
c) The vehicle is either a truck or an SUV. _______
d) The driver is a female. ______
e) Name two events that are mutually exclusive based on this particular data set.
f) Name two events that are not mutually exclusive, based on this data set.
g) Are the events Male & Truck independent? Say yes or no. Then explain why both by showing the math and by a verbal explanation that a non-statistician would understand.
Yes or no? _____
Mathematical explanation:
Verbal explanation:
Car
SUV
Truck
Male
20
45
30
Female
60
35
10
Explanation / Answer
As multiple parts are posted, only the first 4 parts will be answered.
a. P(Male | Car) = N(Male and Car) / N(Car) = 20 / (20+60) = 0.25
b. P(Female and Truck) = N(Female and Truck) / N( Total ) = 10 / 200 = 0.05
c. P(Truck or SUV) = N(Truck or SUV) / N( Total ) = (30+10+35+45) / 200 = 0.60
d. P(Female) = N(Female) / N(Total) = (60+35+10)/200 = 0.525
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