Question

Suppose that MERCEDES COMPANY has announced that some of the cars that they sold( of each of the 3 MODELS X, Y and Z) in NORTH CYPRUS last year (2019) has turned out to be DEFECTIVE.

The respective number of Non- Defective and Total Number of Mercedes cars sold for each Model have been reported to be as follows;

                                                                                                                   MODEL

                                                                                                     X                  Y                    Z

   NUMBER OF NON DEFECTIVE CARS SOLD                     150               50               500

              TOTAL NUMBER OF CARS SOLD                            300              500               800

Suppose that we randomly select 2 different (First and Second) consumers each of whom purchased a new MERCEDES car in 2020. Given this experiment answer all of the following 10 questions.

Q1) What is the probability of the first consumer’s car to be MODEL X?

Q2)What is the probability of the first consumer’s car to be either MODEL Y or MODEL Z?

Q3)What is the probability of the second consumer’s car to be either MODEL X or MODEL Y?

Q4) What is the probability of the first consumer’s car to be either DEFECTIVE or MODEL Y?

Q5) What is the probability of the second consumer’s car to be either NON-DEFECTIVE or MODEL Z?

Q6)If the second consumer’s car is MODEL Y, what is the probability that İt is NON-DEFECTIVE?

Q7) If the first consumer’s car is NON-DEFECTIVE what is the probability that it is MODEL Z?

Q8) What is the probability of the cars of both of these 2 consumers to be DEFECTIVE?

Q9)If the car of the first consumer is MODEL Z what is the probability of the car of the second consumer to be MODEL X?

Q10) If the car of the second consumer is DEFECTIVE, what is the probability of the car of the first consumer to be MODEL Y?

Answer 1

Total number of cars sold = 300 + 500 + 800 = 1600

Total number of non-defective cars sold = 150 + 50 + 500 = 700

So, total number of defective cars sold = 1600 - 700 = 900

Q1) Probability of the first consumer's car to be Model X

Q2) Probability of the first consumer's car to be either Model Y or Model Z

Q3) Probability of the second consumer's car to be either Model X or Model Y

Q4) Probability of the first consumer's car to be either Defective or Model Y. Note we have to subtract the number of cars which are both Defective and Model Y.

Q5) Probability of the second consumer's car to be either Non-Defective or Model Z. Note we have to subtract the number of cars which are both Non-Defective and Model Z.

Q6) Given the second consumer's car is Model Y, probability that it is Non-Defective. We have to only look at the Model Y column to get the answer.

Q7) Given the first consumer's car is Non-Defective, probability that it is Model Z. We have to only look at the Non-Defective row to get the answer.

Q8) Probability of defective car for first consumer = 900/1600.

Given that the first car is defective, probability of defective car for second consumer = 899/1599.

Probability of defective car for both consumers

Q9) Given that the first consumer's car is Model Z, the probability of second consumer's car to be Model X

Q10) The second consumer can either have a Model Y (probability = 450/900 = 1/2) or other model (probability= 450/900 = 1/2).

Given that the second consumer's car is Defective, the probability of first consumer's car to be Model Y