Bad gums may mean a bad heart. Researchers discovered that 81% of people who have suffered a heart attack had periodontal disease, an inflammation of the gums. Only 32% of healthy people have this disease. Suppose that in a certain community heart attacks are quite rare, occurring with only 11% probability. If someone has periodontal disease, what is the probability that he or she will have a heart attack?

Sixty percent of clowns aren’t funny.   If you randomly encounter three different clowns, what is the probability that none of them are funny?

A study showed that in​ 1990, 47​% of all those involved in a fatal car crash wore seat belts. Of those in a fatal crash who wore seat​ belts, 46​% were injured and 26​% were killed. For those not wearing seat​ belts, the comparable figures were 43​% and 51​%, respectively. Find the probability that a randomly selected person who was unharmed in a fatal crash was not wearing a seat belt.

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?

Disco Fever is randomly found in one half of one percent of the general population. Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease. The test also yields a false positive in 4% of the cases where the disease is not present. What is the probability that the disease is absent if the test result is negative?

Suppose that about 55% of the people who are murdered actually knew the murderer. Suppose that a detective file in Boston has 51 current unsolved murders. What is the probability that fewer than 21 victims knew their murderer?

A drug test facility uses a test that has a 1% false negative rate, and a 2% false positive rate. It is estimated that 4% of the population is taking this drug. If a random person who tested positive is chosen, what is the probability that they are actually taking the drug?

Multiple studies conducted in the United States, Canada, Germany, and the United Kingdom show that the probability of dying in the hospital is higher if you are admitted on the weekend. Why might this be? What factors might contribute to this probability?  What could hospitals do to reduce/eliminate this phenomenon?

Empirical evidence suggests that 25% of Florida drivers are uninsured. If four random Florida drivers are involved in an accident, what is the probability that more than one of them are uninsured?