The lifetime risk of developing cancer is about one in 67 (1.5%). Let X = the number of people you ask before one says they have cancer. The random variable X in this case includes only the number of trials that were failures and does not count the trial that was a success in finding a person who had the disease. The appropriate formula for this random variable is the second one presented above. Then X is a discrete random variable with a geometric distribution:
- What is the probability that you ask 9 people before one says they have cancer? This is asking, what is the probability that you ask 9 people who say no and the tenth person says yes?
- What is the probability that you must ask 20 people?
- Find the (i) mean and (ii) standard deviation of X.
OpenStax Introductory Business Statistics 2e, 4.3 Geometric Distribution, exercise 7