Question

Transmission type (A B) , Versions (TD FD HB)

TD FD HB

A 0.32 0.27 0.18

B 0.08 0.04 0.11

A customer is selected randomly  What is the probability that this customer purchased a car with an automatic transmission? A four-door car? A car with an automatic transmission and four doors?

 Given that the customer purchased a four-door car, what is the probability that it has an automatic transmission?

 Given that the customer did not purchase a hatchback, what is the probability that the car has a manual transmission?

Please show all work and explain why its independent or dependent. Also please include a tree diagram if it is possible

Answer 1

Transmission type (A B) , Versions (TD FD HB)

	TD	FD	HB
A	0.32	0.27	0.18
B	0.08	0.04	0.11

It is not clear in the question that transmission types A and B are Automatic or Manual. I am assuming that A is automatic and B is manual.

(1) Probability that a randomly selected customer purchased a car with automatic transmission = 0.32 + 0.27 + 0.18 = 0.77.

Probability that a randomly selected customer purchased a car with four doors = 0.27 + 0.04 = 0.31. These events are dependent as four door cars can be with automatic transmission or manual transmission, these events are mutually exclusive.

Probability that a randomly selected customer purchased a car with automatic transmission and four doors = 0.27. These events are independent.

(2) Given that the customer purchased a four-door car, then probability that it has an automatic transmission is given by

(3) Not purchasing Hatch back means, customer purchased some other version (may not be mentioned in the table) and its probability = 1 - P(HB)