#1. in the state of MN with a a fairly large population, a recent study showed that 34% of the people who got a flu shot.flu vaccination last year. Give 4 decimal place accuracy on answers. a) If one

#1. in the state of MN with a a fairly large population, a recent study showed that 34% of the people who got a flu shot.flu vaccination last year.  Give 4 decimal place accuracy on answers.

a) If one person in Minnesota is selected at random, what is the probability they did not get a flu shot last year?

b) If 2 Minnesotans are selected at random, what is the probability that they both got the flu shot?

c) if 4 people are randomly selected from across Minnesota, what is the probability that AT LEAST ONE of the got the flu shot?

#2 In rural Texas a recent study from the university of Austin showed that 84% of the houses need a new roof; 72% of the houses have trees in the yard. If it needs a new roof, what is the probability that a particular house in Texas has trees in the year? Round to 4 decimal place accuracy.

#3 The epic corporation utilizes a training program to target employees that it hires and strategically place them into apocopate jobs within the company. The program consists of two steps, and each step has built in quotas. Step I of the program identifies 40% of the hires as management trainees, 45% as non-managerial trainees, and the rest will be fired. In Step II of the program 75% of the management trainees are assigned to managerial positions. 20% are assigned to non- managerial positions, and the others are fired. Also i, in Step II half of the non-managerial trainees are retained as workers in the same category position, but the rest are fired

a) Construct a tree diagram for this situation labeled with suitable probabilities. Be complete and organized

b) What is the probability that a randomly chosen hiree will have been fired by the end of the training period? Show your work.

#4 AMES Engineering Inc is a small engineering firm that works with NASA. According to human resources, there are 22 engineering team members at the firm including : 7 men, 14 women, plus the team supervisor is a woman named Lois Jordan. SHOW ALL WORK> 

a) At AMES Engineering Inc., in how many ways can a 5-person committee be chosen from the entire engineering team to analyze a new project? Show your work.

b) if a 5-person committee is chosen at random at AMES Engineering , what is the probability that it contains 3 men and 2 women from the engineering team? You must show how you computed your answer Give answer accurately to 4 decimal places.

C) if a 5-person committee is chosen at random from the engineering team, what is the probability that Lois Jordan is choses as part of the committee? You must show how you computed your answer. Give answer accurately to 4 decimal places.