6.3 Calculating Probabilities of EventsEx 1: Selecting Balls from an Urn: An urn contains eight white balls and two green balls. A sample of three balls is selected at random. What is the probability of selecting only white balls?

Ex 2: Using the situation above, what is the probability that the sample contains at least one green ball?

Ex 3: Quality Control: A toy manufacturer inspects boxes of toys before shipment. Each box contains 10 toys. The inspection procedure consists of randomly selecting three toys from the box. If any are defective, the box is not shipped. Suppose that a given box has two defective toys. What is the probability that it will not be shipped?

Ex 4: Selecting Students: A professor is randomly choosing a group of three students to do an oral presentation. In her class of 10 students, 2 are on the debate team. What is the chance that the professor chooses at least one of the debaters for the group?

Ex 5: Medical Screening: Suppose that a cruise ship returns to the United States from a tropical place. Unknown to anyone, 4 of its 600 passengers have contracted a rare disease. Suppose that the Public Health Service screens 20 passengers, selected at random, to see whether the disease is present aboard ship. What is the probability that the presence of the disease will escape detention?

Ex 6: The Famous Birthday Problem: A group of five people is to be selected at random. What is the probability that two or more of them have the same birthday?

Health statistics: In health stats, the likelihood that something will happen is typically called the risk rather than the probability/chance. Suppose that a study produced the following results: out of a group of 1000 people who at 1.75oz of chocolate per week, 39 had a stroke during a certain time period. IN a control group of 1000 who didn’t each chocolate regularly, 50 had a stroke during the same time period. There are three ways to report the benefit of eating chocolate. Absolute Risk Reduction: Relative risk reduction:

The number needed to treat method would report the number of people who must participate in the treatment in order to prevent one stroke. ________________were helped, that is one out of 1000/11 (approx 91). Therefore, the number needed to treat is 91.

The researcher would most likely report that eating chocolate reduced the risk of stroke by __________ since that number is more impressive than the other two. Drug advertisements typically report the relative risk reduction.