1. In a group of forty individuals, ten are healthy while the other thirty all have either high blood pressure, high cholesterol, or both. If 15 individuals have hypertension and 25 have hypercholesterolemia, a) how many people have both hypertension and hypercholesterolemia?

What is the chance that a random member of this group would have high blood pressure (event A)?

c) has a high cholesterol level (event B)?

d) has hypertension and a high cholesterol level (events A and B)?

e) has either hypertension or a high cholesterol level (event A or B)?

f) Utilize the preceding to verify the probability formula: P(A or B) equals P(A) + P(B) minus P (A and B).

2.A five-person committee will be selected at random from a group of ten women and six men. Calculate the likelihood that the committee has

a) Three females and two males.

a) Four ladies and one man.

c) Five females.

c) at least three females.

3. In a typical school, 60% of students have access to the internet at home. A random group of eight pupils is selected. Calculate the likelihood that a) precisely five people have internet access.

b) at least six pupils have internet access.

4. A group of 1000 students' scores on a test are regularly distributed, with a mean of 70 and a standard deviation of 10. A random student is chosen from this group.

a) Calculate the likelihood that his/her grade is over 80.

b) Calculate the likelihood that his/her grade is less than 50.

c) Calculate the likelihood that his/her grade is in the range of 50 to 80.

c) How many pupils have grades higher than 80?