In class problem: Privacy is a concern for many villagers surveyed by an environmental scientist. One survey showed that 59% of villagers are somewhat concerned about the confidentiality of their answers about the impact of polyester waste in their brook. Based on this information, what is the probability that for a random sample of 10 villagers, 6 are concerned about answers' confidentiality?

1. A biologist is studying a new genetically engineered lime. It is known that the seeds of this GE lime have probability 0.70 of germinating. The biologist plants six seeds.

a. What is the probability that exactly four seeds will germinate? Make sure to use the formula for this one.

b. What is the probability that at least four seeds will germinate?

2. If 30% of the nurses in your Hospital use the Hospital's Library in one year, find the probability that in a random sample of 15 nurses:

(a) At most 7 use the Library,

(b) At least 5 use the Library,

(c) No more than 2 use the Library

(e) Exactly 7 use the Library

3. One-third of all deaths are caused by heart attacks. If three deaths are chosen randomly, find the probability that none resulted from heart attack.