According to CDC estimates, more than 2.8million people in the United States are sickened each year with antibiotic‑resistant infections, with at least 35,000 dying as a result. Antibiotic resistance occurs when disease‑causing microbes become resistant to antibiotic drug therapy. Because this resistance is typically genetic and transferred to the next generations of microbes, it is a very serious public health problem. Of the infections considered most serious by the CDC, gonorrhea has an estimated 1.14 million new cases occurring annually, and approximately 50%of those cases are resistant to any antibiotic. Assume a health clinic in California sees 10 patients with gonorrhea in a given week.

(c) Find the probability that exactly one of the cases is resistant to any antibiotic. Give your answer to four decimal places.

What is the probability that at least one case is resistant to any antibiotic? (Hint: It is easier to first find the probability that exactly zero of the 1010 cases were resistant.) Give your answer to four decimal places.