PLEASE SHOW YOUR WORK IN EACH QUESTION AND SUB QUESTION.

***Question 1

A class of 50 students obtained the following grades in a statistics course:

A 5 B 25 C 15 D 5

If one student is selected at random, what is the probability that

a. the student obtained a B? 1 marks

b. the student obtained either a B or a C? 2 marks

c. the student did not obtain a D? 2 marks

d. the student did not obtain either a B or a C? 2 Marks

***Question 2 A realty company has 100 homes listed for sale. Some of these homes havefireplaces, some have garages, and some have neither. A breakdown is provided in the two-way classification table below.

FIREPLACE ( F) NO FIREPLACE( F-) GARAGE( G) 50 30 NO GARAGE ( G-) 10 10

a. If one of these 100 homes is selected at random,

i. what is the probability that the home selected does not have a fireplace? 1 marks

ii. what is the probability that the home selected has a fireplace or a garage? 3 marks

iii. what is the probability that the home selected has neither a fireplace nor a garage? 2 marks

iv. what is the probability that the home selected has a garage but not a fireplace? 2 marks

v. what is the probability that the home selected has a garage, given that it has a fireplace?2 marks

b. Are the events F= Fireplace, and G= Garage; independent or dependent? Show your proof. 4 marks

c. Are the events F and G mutually exclusive? Why? 2 marks