The admission fee to a summer fair is $1 for children and seniors, and $3 for adults. Based on previous years, 65% of all visitors to the fair are adults. If 40 entrance tickets to the fair are purchased during a particular period, let X be the corresponding number of children and seniors. (a) What is the distribution of X? (b) What is the expected total ticket revenue during the period? (c) What is the variance of the total ticket revenue during the period?

A prominent physician claims that 70% of patients with lung cancer are chain smokers. (a) Suppose that 10 patients with lung cancer are admitted to a hospital. Calculate the probability that fewer than half of the patients are chain smokers. (b) Suppose that 10 patients with lung cancer are admitted to a hospital. Calculate the probability that fewer than half of the patients are chain smokers.