Can you please check the answer below, I find these probability questions confusing and it gets hard to know what the question is asking? would you suggest an easy way to understand and resolve these kinds of problems?
A question that I am struggling with at the moment:
The automobile industry sold 657,000 vehicles in the United States during January 2009 (The Wall Street Journal, February 4, 2009). This volume was down 37% from January 2008 as economic conditions continued to decline. The Big Three U.S. automakers—General Motors, Ford, and Chrysler—sold 280,500 vehicles, down 48% from January 2008. A summary of sales by automobile manufacturer and type of vehicle sold is shown in the following table. Data are in thousands of vehicles. The non-U.S. manufacturers are led by Toyota, Honda, and Nissan. The category Light Truck includes pickup, minivan, SUV, and crossover models.
Type of Vehicle Car Light Truck Total U.S 87.40 193.10 280.50 Manufacturer Non-U.S 228.50 148.00 376.50 Total 315.90 341.10 657.00
a. Develop a joint probability table for these data and use the table to answer the remaining questions.
Joint Probability Table Car Light Truck Total U.S 0.1330 0.2939 0.4269 Non-U.S 0.3478 0.2253 0.5731 Total 0.4808 0.5192 1.0000
b. What are the marginal probabilities? What do they tell you about the probabilities associated with the manufacturer and the type of vehicle sold?
.5731 vs .4269 (Non-US is slightly higher)
.4808 vs .5192 (Light Truck is slightly higher)
c. If a vehicle was manufactured by one of the U.S. automakers, what is the probability that the vehicle was a car? What is the probability it was a light truck?
P(US & Car) 87.4/280.5 = 0.3116. P(US & Light truck) 193.1/280.50 = .6884
d. If a vehicle was not manufactured by one of the U.S. automakers, what is the probability that the vehicle was a car? What is the probability it was a light truck?
P(Non-us & Car) 228.5/376.5 = 0.6069. P(Non-US & Light Truck) 148.0/376.5 = 0.39301
e. If the vehicle was a light truck, what is the probability that it was manufactured by one of the U.S. automakers?
P(Light Truck & US) = 193.1/341.1 = 0.5661
f. What does the probability information tell you about sales?
Tells us that US is slightly higher in sales for Light Truck and quiet low for Cars in comparison to Non US.
Thanks in advance