I found you online.......

Can you help with empirical probability?


Hi Partha. I really liked your email that you sent me, it really inspired me. I have been breezing through the chapters, and doing quite well, You should be a teacher. After all the time my college instructor spent with the class on the slopes etc.... There were very few of us who really understood it. However, after reading your notes and seeing how you worked the problems and the way you explained it, Not only do I completely understand, but I have shared the information with many of my classmates and they too finally understand.  You definately have a gift, not only being so intelligent , but to also have the gift of teaching it so is so impressive.

I am having some problems understanding some of the questions in my homework that are about empirical probability.  If you can find the time, send me some information on these two problems, because I haven't even been able to get started good, I am so confused.

Thanks,
Cassie
        1.. Estimate the probability that a randomly selected adult 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 

          3.  Yahtzee is a game that is played by rolling 5 dice at once.  The object of the game is to be the first to roll various combinations of                       numbers (like five 5's or three of one number and two of another at the same time).  This is all explained in the rules of Yahtzee.  

              Read the rules of Yahtzee and determine the following probabilities:

           a.    P(five 5's) =                            {called "five of a kind" in the game} 
           b.    P(five of any number) =           {called "five of a kind"} 
           c.    P(three of one number and two of another) =         {a "full house"} 
           d.    P(rolling a "straight") =                                           {1, 2, 3, 4, 5 or 2, 3, 4, 5, 6} 
           e.    P(three 4's) =                                                        {called "three of a kind"} 
           f.     P(filling in all rows on the game card on consecutive tosses) =


      I have included the only information that they gave me on Empirical Probability:

      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. 
     




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