relationship beween vitamin supplementation and the occurrence of asthma

Alpha6

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Oct 21, 2013
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The question is:

a study was conducted on the relationship beween vitamin supplementation and the occurrence of asthma among cildren. The investigators found that compared with children who did not take vitamins, children who took vitamins on a daily basis were 0.8 times as likely to develop asthma. This means that children who took vitamins were 80% less likely to develop asthma.



The answer was actually False. I do not understand how. If they are .8 times more likely to remain healthy, aren't they 80% less likely to get it?
 
Often times with probability problems, I find it easiest to consider the most extreme cases and work from there. For this problem, let's assume that the base probability of a child not taking vitamins to develop asthma was 1. That is to say, every child who do not take vitamins will develop asthma. The problem tells us that children who do take vitamins are "0.8 times more likely to develop asthma." What expression would you create to model this piece of information? What, then, is the probability be of children taking vitamins to develop asthma?

Now, we're also told (assuming the statement is true) that "children who took vitamins were 80% less likely to develop asthma." What expression would you use to model this piece of information? When thinking about this, remember that 1 is the same as 100%. Again, assuming the statement is true, what would the probability be of children taking vitamins to develop asthma? Does this agree with the conclusion you came to earlier? What does that suggest about whether the statement is true or not?
 
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