.Records show that 70% of the students preparing for the high school equivalency exam need help in math, 60% need help in English, and 45% need work in both. If a student is randomly chosen, find the probability that the person needs help in math or English.

a)Use the General Addition Rule to find the probability that a randomly chosen student needs help in math or English.

b)

Venn Diagram

Create a Venn Diagram of the problem.

c)Find P(Math but not English).

d)Use the diagram to find P(Math or English).

e)Find P(neither Math nor English).

3.A utility company in a large metropolitan area finds that 95% of its customers pay a given monthly bill in full. Looking more closely at their records, they find that 98% of the customers who pay one monthly bill in full will also pay the next monthly bill in full. Only 10% of those who pay less than the full amount one month will pay in full the next month.

a)Create a tree diagram.

b)Find the probability that a customer chosen at random will pay two consecutive months in full.

c)Find the probability that a customer selected at random will pay neither of two consecutive months in full.

d)Find the probability that a customer chosen at random will pay exactly one month in full.

e)If a person paid the second month in full, what is the probability that they also paid the first month in full?

4.Suppose that out of 120 students, 10 complete 10^thgrade (10 years of school), 50 complete high school (12 years of school), 45 complete college (16 years of school), and the rest complete a Ph.D. (20 years of school).

a)Complete the following probability model for the number of years of schooling students complete.

Number of Years of School

Probability

b)Find the expected number of years of schooling for this group of students.

5. :Ten customers enter a clothing store during a one-hour period. Past experience has shown that approximately 30% of the people entering the store make a purchase.

a)What conditions must be met before applying a binomial distribution model? Are those conditions met in this scenario?

b)What is the probability that exactly 6 customers make a purchase?

c)What is the probability that at least one customer makes a purchase?

d)What is the probability that no more than 8 customers make a purchase?

e)What is the probability that between 4 and 8 customers (inclusive) make a purchase?