Statistics

1. Find an example of probability in a recent news article. Does the usage of probability in the article lend itself more to a frequency- based or belief-based interpretation? Would the writer or person quoted agree that probability is a measurable property of the system being described? Now try to find an opposite example, i.e., if your previous example was more frequency-based, try to find a belief-based example, and vice versa.

2. Which is more probable: rolling at least one six in four rolls of a fair die, or rolling at least one double-six in 24 rolls of a pair of dice? Be sure to explain every step of your derivation, and state any assumptions you are making.

3. A weather forecaster on the evening news says, “Tomorrow’s chance of rain is 80%.” It doesn’t rain the next day. Was the forecast right or not? The same forecaster goes on the evening news every day for a year and says the same thing — tomorrow’s chance of rain is 80% — but it never rains. Were any of the forecasts right? Which ones?