Questions 16-20 concern the following setting. A car comes equipped with either
ID: 3238326 • Letter: Q
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Questions 16-20 concern the following setting. A car comes equipped with either an automatic or a manual transmission, and the car is available in one of four colors. A population of 100 such cars has the following numbers of cars with these characteristics:
White Blue Black Red
Automatic 15 10 10 10
Manual 15 5 1 5 20
Suppose that one car is randomly selected from the above population.
16. What is the probability that the car is red? (A) 0.10 (B) 0.20 (C) 0.30 (D) 0.40 (E) None of these
17. What is the probability that the car has automatic transmission? (A) 0.15 (B) 0.30 (C) 0.45 (D) 0.55 (E) None of these
18. What is the probability of selecting a red car with automatic transmission? (A) 0.100 (B) 0.165 (C) 0.200 (D) 0.300 (E) None of these
19. What is the probability that a selected car has automatic transmission, given that the car is red? (A) 1 10 (B) 2 9 (C) 2 11 (D) 1 3 (E) None of these
20. Compute the expected value of X, where X is a random variable indicating selecting a red car (that is, X = 1 if the car is red and X = 0 if the car is not red). (A) 0.03 (B) 0.3 (C) 3 (D) 30 (E) None of these
Questions 16-20 concern the following setting. A car comes equipped with either an automatic or a manual transmission, and the car is available in one of four colors. A population of 100 such cars has the following numbers of cars with these characteristics: White Blue Black Red Automatic 15 10 10 10 15 5 15 20 Suppose that one car is randomly selected from the above population. 16. What is the probability that the car is red? (A) 0.10 (B) 0.20 (C) 0.30 (D) 0.40 (E) None of these 17. What is the probability that the car has automatic transmission? (A) 0.15 (B) 0.30 (C) 0.45 (D) 0.55 (E) None of these 18. What is the probability of selecting a red car with automatic transmis- Sion. (A) 0.100 (B) 0.165 (C) 0.200 (D) 0.300 (E) None of these 19. What is the probability that a selected car has automatic transmission, given that the car is red? (A) 10 (B) (C) 11 (D) L (E) None of these 20. Compute the expected value of X, where X is a random variable indi- cating selecting a red car (that is, X J 1 if the car is red and X 0 if the car is not red). (A) 0.03 (B) 0.3 (C) 3 (D) 30 (E) None of theseExplanation / Answer
Total cars = 100
16. Total red cars =30 ; probability= (30/100)= 0.30
17. Total automatic transmission cars=45; probability= (45/100)= 0.45
18. No of red automatic transmission are = 10; probability= (10/100)= 0.10
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