Suppose that lesions are present at 5 sites among 50 in a patient. A biopsy selects 8 sites randomly (without replacement).
a. What is the probability that lesions are present in at least one selected site?
b. What is the probability that lesions are present in two or more selected sites?
c. Instead of eight sites, what is the minimum number of sites that need to be selected to meet the following objective? The probability that at least one site has lesions present is greater than or equal to 0.9.

Q68;

A utility company might offer electrical rates based on time-of-day consumption to decrease the peak demand in a day. Enough customers need to accept the plan for it to be successful. Suppose that among 50 major customers, 15 would accept the plan. The utility selects 10 major customers randomly (without replacement) to contact and promote the plan.
a. What is the probability that exactly two of the selected major customers accept the plan?
b. What is the probability that at least one of the selected major customers accepts the plan?
c. Instead of 15 customers, what is the minimum number of major customers that would need to accept the plan to meet the following objective? The probability that at least one selected major customer accepts the plan is greater than or equal to 0.95.