A sample of 500 large companies showed that 120 of them offer free psychiatric help to their employees who suffer from psychological problems. If one company is selected at random from this sample, what is the probability that this company offers free psychiatric help to its employees who suffer from psychological problems? What is the probability that this company does not offer free psychiatric help to its employees who suffer from psychological problems?

An article was published recently suggesting that persons who exercise regularly can reduce their risk of major clinical events (e.g. diabetes, cardiovascular disease) by up to 50% in some instances. It is believed that only 30% of adult Americans exercise on a regular basis. If eight adult Americans are analyzed, what is the probability that less than half of them exercise regularly? For some reason, I keep coming out with the wrong numbers.

Apparently, depression significantly increases the risk of developing dementia later in lift (BBC News, July 6, 2010). In a recent study it was reported that 22% of those who had depression went on to develop dementia, compared to only 17% of those who did not have depression. Suppose 10% of all people suffer from depression.   What is the probability of a person developing dementia?   If a person has developed dementia, what is the probability that the person suffered from depression earlier in life?

The Pew Research Center has found that 86% of people 18 through 29 years old are social media users. What is the probability that you have to ask 10 people in this age group to find one that is not a social media user?What is the probability that you have to ask 20 people in this age group to find one that is not a social media user?What is the probability you must ask at most 5 people in this age group to find one that is not a social media user?