Samples of rejuvenated mitochondria are mutated (defective) in 3% of cases. Suppose 16 samples are studied, and they can be considered to be independent for mutation. Determine the following probabilities. (a) No samples are mutated. (b) At most one sample is mutated.

A new surgery is successfully 85% of the time . If the results of 7 such surgeries are randomly sampled, what is the probability that at least 5 of them are successful. Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places.

A test to determine whether a certain antibody is present is 99.4% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject) 99.4% of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is 0.006. Suppose the test is given to seven randomly selected people who do not have the antibody. (a) What is the probability that the test comes back negative for all seven people? (b) What is the probability that the test comes back positive for at least one of the seven people?

A diagnostic test for disease X correctly identifies the disease 88% of the time. False positives occur 11%. It is estimated that 2.78% of the population suffers from disease X. Suppose the test is applied to a random individual from the population. Compute the following probabilities.                                                                                                                                                                                                                                                                                                   The percentage chance that, given a negative result, the person does not have disease X=                                        The percentage chance that, the person will be misclassified =