Here is the first one..:The work has to be shown though... can't just have the answers..
Introduction
A probability may be a very complicated number to compute. It is reasonably easy to use theoretical methods when computing probabilities involving decks of cards and coin tosses because you can often list or easily count all the possible ways a desired outcome might occur.
However if you pose a question such as "What is the probability of an auto accident?" it becomes impossible to consider all the factors involved. A theoretical analysis of this question would involve consideration of every way an auto accident could occur (already a daunting task), knowledge of the driving skills of every driver, the driving patterns of all drivers and the chances a bad or careless driver would encounter another driver at precisely the right instant to cause an accident. Techniques involving empirical data must be used.
An Empirical Probability
If a coin is a fair coin, then you would expect the number of heads to be roughly half the number of times you tossed it. Here you are using the theoretical probability of = for a head. If you suspected a coin was slightly top heavy how would you compute the probability of a head? You have no theory at your disposal.
The answer is, you would flip the coin a lot (emphasis on "a lot") and count the number of heads. If you flipped the coin 1,000 times and saw 650 heads, you would estimate the probability of a head to be 650/1000 = 0.65 . This might not be the exact probability. Flipping 10,000 times might reveal 6486 heads or a probability of 0.6486 but you would be confident your estimate was close.
This is how probabilities are often computed for events far too complicated to analyze theoretically. For example, consider a health-related probability. The National Center for Health Statistics, a division of the Center for Disease Control, (
http://www.cdc.gov/nchs) collects and publishes data of a health related nature. The web site mostly contains data that have been already statistically summarized along with a variety of factoids. The "FASTATS A to Z" link off the main page leads to an alphabetical list of topics that are interesting to peruse.
For instance, a look at the comprehensive data under Allergies reveals the fact that in 1997, there were 18.092 million cases of hay fever in the US among people 18 years of age or older, in other words, among adults. How would we convert this to a probability?
To compute the probability of hay fever, we would need to divide the number of observed cases with the number of possible cases, i.e. the population. Note that our hay fever data refers specifically to people of a certain age group not the entire population. Therefore we need the adult U.S. population in 1997, since this is the year the hay fever number was collected. A visit to the Census bureau web site (
http://www.census.gov) provides us with an estimate of 198.18 million adults in the U.S. in 1997. Thus we estimate
Probability of hay fever:
.
Note that due to the large amount of time needed to accurately collect such health and census data, we often have to use data from a number of years prior to the current year in these estimates. The exercises will have you seek out similar data to estimate probabilities.
When you are finished reviewing this Project, go on to the exercises below.
1. Estimate the probability that a randomly selected person in the U.S. will be afflicted with asthma. Use this probability to estimate the number of Americans afflicted in 2000.
2. A Web Search Exercise Using data from any year in the last 10 years, estimate the probability a newborn baby will be female. Locate the necessary data on the World Wide Web and submit the relevant URLs along with your answer. Here is a link to a U.S. census page that has some data on population and gender statistics: Male-Female Ratio
Linear Mode
