***Question 3

A person has applied for positions at Company A, Company B, and Company C. The probability of obtaining an offer from Company A is 0.4,from Company B is 0.3, and from Company C is 0.6. Assume that the three job offers will be independent.

a. What is the probability that the person will receive job offers from all three companies? 2 marks

b. What is the probability that the person will receive a job offer from Company B only? 2 marks

c. What is the probability that the person will receive a job offer from atleast one of the three companies? 2 marks

d. What is the probability that the person will receive exactly one job offer from the three companies? 4 marks

AlsoConstruct a tree diagram please.

***Question 4

A city council consists of 7 males and 4 females. Two councilors are selectedat random to represent the city at an Elton John concert. What is the probability that

a. both councilors are male? 2 marks

b. one councilor is a male and one a female?5 marks

c. at least one councilor is a female?2 marks

AlsoConstruct a tree diagram please.

Note: Express probabilities to 4 decimal places of accuracy.Hint: Construct a tree diagram.