Carib Cement Ltd. manufactures cement at two plants, one in Barbados and the other in Trinidad. The Barbados plant has 50 employees and the Trinidad plant has 75. A random sample of 10 employees is asked to fill out a satisfaction survey.
(i) What is the probability that none of the employees in the sample work at the plant in Barbados?
(ii) What is the probability that one of the employees in the sample works at the plant in Barbados?
(iii) What is the probability that nine of the employees work at the plant in Barbados?