A sample of 4 different calculators is randomly selected from a group containing 16 that are defective and 28 that have no defects. What is the probability that at least one of the calculators is​ defective?

In a study of 235,722 cell phone users, it was found that 109 developed cancer of the brain or nervous system. Assuming that cell phones have no effect, there is a 0.000477 probability of a person developing cancer of the brain or nervous system. We therefore expect about 113 cases of such cancer in a group of 235,722 people. Estimate the probability of 109 or fewer cases of such cancer in a group of 235,722 people. What do these results suggest about media reports that cell phones cause cancer of the brain or nervous system? (a) P(x ≤ 109) = (Round to four decimal places as needed.)

A pharmaceutical company is running trials on a new test for anabolic steroids. The company uses the test on 400 athletes known to be using steroids and 200 athletes known not to be using steroids. Of those using steroids, the new test is positive for 375 and negative for 25. Of those not using steroids, the test is positive for 25 and negative for 175. What is the relative frequency of a false negative result (the probability that an athlete using steroids will test negative)? (Round your answer to two decimal places.) What is the relative frequency of a false positive result (the probability that an athlete not using steroids will test positive)? (Round your answer to two decimal places.)

Suppose that if person with tuberculosis is given a TB screening, the probability that his or her condition will be detected is 0.90. If a person without tuberculosis is given a TB screening , the probability that he or she will be diagnosed incorrectly as having tuberculosis is 0.3. Suppose, further, that 11% of the adult residents of a certain city have tuberculosis. If one of these adults is diagnosed as having tuberculosis based on the screening, what is the probability that he or she actually has tuberculosis?

The hospital records show that 75% of patients suffered from COVID-19 dies. What is the probability that 4 out of 6 randomly selected patients will recover?