Question

A new test for detecting breast cancer is negative in 95% of patients who do not have the disease. If the test is used with 8 consecutive blood samples taken from patients with out the disease what is the probability of getting at least one positive test result? What is the probability of getting 8 positive test results? If 20% of a given population suffers from hypertension and 10% from hypotension, the probability that a randomly selected member of this population will suffer from one of these ailments is _______.  If 20% of a given population suffers from hypertension and 10% from hypotension, the probability that a randomly selected member of this population will suffer from both of these ailments is ____________.

Answer 1

P(negative test result if one person is not having disease) = 0.95

P(at lest one positive result) = 1 - P(all negative results)

= 1 - 0.95⁸

= 0.3366

P(8 positive results) = (1 - 0.95)⁸

= 3.9x10^-11

Assuming that the events are mutually exclusive,

P(a person will suffer from one of these ailment) = P(hypertension) + P(hypotension)

= 0.20 + 0.10

= 0.30

P(a member will suffer from both) = 0