People With the Same Birthday:
Calculating Probability
- colors in a jar
- letters in the alphabet
- Scientists and sampling (fish in a pond; population in the U.S.)--sampling can actually be used to estimate the number of people with HIV!
Directions:
Some things are sure to happen. If today is Monday, tomorrow will be Tuesday. Some things are impossible. You can't roll a seven with only one of a pair of dice. Some things may or may not happen. Maybe it will snow, maybe it won't.
With each of the following statements, choose S for sure, I for impossible, or M for maybe.
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There is a live dinosaur in the zoo.
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You will get tails if you toss a coin.
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It will rain on Saturday.
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Superman will always beat the bad guys.
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The next time you throw an ordinary ball, it will keep going up into space.
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Someone will win a state lottery twice in one year.
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When you grow up, you will be ten feet tall.
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Outdoors at night you can see the stars in the sky.
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Your Little League team will win its next game.
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The earth revolves around the sun.
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You will be in school tomorrow.
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In a new box of crayons, at least one will be red.
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Does everyone agree on which things are for sure and which are not?
Should everyone agree?
Why or why not?
Explore other topics:
Links
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To estimate the number of people infected with H.I.V., statitisticians look at the percentage of people who test positive. Since not everyone has been tested, the people who have been tested are a sample population. If this sample is representative of the total population, the statisticians just need to know what percentage of people have been tested. Then the percent of people who test positive must be multiplied by a number that shows the ratio of the total population to the number of people who have actually been tested.
However, since much testing is anonymous, and since individuals can be retested repeatedly, it's not all that easy to calculate the percentage of people actually tested, at last! The number tested could represent one person testing over and over again, or many different people. So another sample group of the population must be surveyed, to ask its members whether or not they have been tested for H.I.V., and from this sample, the percentage of people in the total population who have been tested can be estimated. (In a recent U.S. study, most people surveyed said they had not been tested for H.I.V. Were these people surveyed representative of people in the U.S. or not? If they were representative of people in the U.S., statisticians might use this sample to calculate the number of people in the U.S. who have been tested!)
Of course, statisticians always estimate; they cannot calculate an exact number; they are just guessing; also, people still in the window period who test negative even though they have been infected with H.I.V. will not be counted accurately!
Two things that are important in sampling:
Is the sample representative of the total population? Is it like it in hobbies, age, activities, income, gender, etc.?
Is the sample large enough to really represent the population? Larger samples generally are more likely to represent a population accurately, and generally give better estimates!
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