Question

MODEL

X Y Z

NUMBER OF DEFECTIVE CARS SOLD 50 100 350

TOTAL NUMBER OF CARS SOLD 150 250 600

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 Z?

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

Suppose, D denotes the event that a car is defective.

The 2*3 contingency table is as follows.

Observed frequences	X	Y	Z	Total
Defective	50	100	350	500
Non defective	100	150	250	500
Total	150	250	600	1000

1.

Required probability is given by

2.

Required probability is given by

3.

Required probability is given by

4.

Required probability is given by

5.

Required probability is given by

6.

Required probability is given by

7.

Required probability is given by

8.

For first consumer there are 1000 cars and 500 defectives. When car of first consumer is defective, there are 999 remaining cars out of which 499 cars are defective.

So, required probability is given by

9.

For first consumer there are 1000 cars, out of which 600 are of model Z. For the second consumer there are 999 cars left, out of which 150 are of model X.

So, required probability is given by

10.

Required conditional probability is given by

Now,